Related papers: Trees within trees II: Nested Fragmentations
We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar…
The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and…
A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting…
We assume that, in equilibrium, nuclear matter at reduced density and moderate finite temperature, breaks up into many fragments. A strong support to this assumption is provided by date accumulated from intermediate energy heavy ion…
We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes…
Given a general critical or sub-critical branching mechanism and its associated L\'evy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the…
The asymptotic behavior, as $n\rightarrow \infty $ of the probability of the event that a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),...,Z_{N}(m)),$ $m=0,1,2,...,$ with $N$ types of particles dies at moment $n$ is…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
We study the rate of weak convergence of Markov chains to diffusion processes under suitable but quite general assumptions. We give an example in the financial framework, applying the convergence analysis to a multiple jumps tree…
How does a shell explode into a series of fragments upon impact? The well accepted explanation is Mott's theory, which considers the fragmentation of shells as a random process controlled by defects. However, Mott's theory is inadequate due…
We investigate the shrinkage induced breakup of thin layers of heterogeneous materials attached to a substrate, a ubiquitous natural phenomenon with a wide range of potential applications. Focusing on the evolution of the fragment ensemble,…
Coalescent models of bifurcating genealogies are used to infer evolutionary parameters from molecular data. However, there are many situations where bifurcating genealogies do not accurately reflect the true underlying ancestral history of…
A Markov evolution of a system of point particles in $\mathbb{R}^d$ is described at micro-and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the influence of each other…
This survey gives an overview over different techniques used for pixel-level semantic segmentation. Metrics and datasets for the evaluation of segmentation algorithms and traditional approaches for segmentation such as unsupervised methods,…
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…
A system of interacting multiclass finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-colors nodes. The interaction is local and described through…
Ice-templating is a well-established processing route for porous ceramics. Because of the structure/properties relationships, it is essential to better understand and control the solidification microstructures. Ice-templating is based on…
Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of…
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…