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Anh Duc Vu

Publications and source records attributed to Anh Duc Vu.

11 recordsLinked to original sources
arXiv2026

Convex order and faster transmission in first contact percolation

Inspired by strict-monotonicity criteria for the time constant in first passage percolation, we investigate convex ordering of point processes in relation to the time constant in first contact percolation. In a nutshell, first contact percolation models the spread of an infection as a contact process without recovery based on a generalized graphical representation, where the usual homogeneous Poisson point processes on the edges are replaced by general simple point processes. Based on a notion of convex ordering for point processes, we prove monotonicity in the number and existence of infection paths. We argue that this convex ordering is however not enough to ensure strict monotonicities in the asymptotic speed of the infection. Instead, we propose a criterion based on an ordering of void probabilities and prove a speed-up for one-dimensional systems based on $\mathbb{Z}$-stationary point processes.

math.PR↗
arXiv2026

Detection, coverage and percolation in dynamic Boolean models with random radii based on $α$-stable processes

We consider a dynamic network in continuum time and space in which nodes, with initial locations given by a Poisson point process, move according to i.i.d. isotropic $α$-stable processes. Each node is additionally equipped with an i.i.d. detection radius. Inspired by corresponding results by Peres et. al. on mobile networks based on Brownian sausages with fixed width, we investigate the tail behaviour of three stopping times: The detection time of the first discovery of a designated node, the first coverage of an entire set, and the first discovery of a node by the infinite connected component of the system. Broadly speaking, we discover that the stability index as well as the random radii manifest themselves only in constants in the otherwise exponential decay rates. The proofs rest on heat-kernel bounds for the underlying Lévy processes and a detailed multiscale analysis allowing us to control the space-time correlations of the system.

math.PR↗
arXiv2025

First contact percolation

We study a version of first passage percolation on $\mathbb{Z}^d$ where the random passage times on the edges are replaced by contact times represented by random closed sets on $\mathbb{R}$. Similarly to the contact process without recovery, an infection can spread into the system along increasing sequences of contact times. In case of stationary contact times, we can identify associated first passage percolation models, which in turn establish shape theorems also for first contact percolation. In case of periodic contact times that reflect some reoccurring daily pattern, we also present shape theorems with limiting shapes that are universal with respect to the within-one-day contact distribution. In this case, we also prove a Poisson approximation for increasing numbers of within-one-day contacts. Finally, we present a comparison of the limiting speeds of three models -- all calibrated to have one expected contact per day -- that suggests that less randomness is beneficial for the speed of the infection. The proofs rest on coupling and subergodicity arguments.

math.PR↗
arXiv2023

A long-range contact process in a random environment

We study survival and extinction of a long-range infection process on a diluted one-dimensional lattice in discrete time. The infection can spread to distant vertices according to a Pareto distribution, however spreading is also prohibited at random times. We prove a phase transition in the recovery parameter via block arguments. This contributes to a line of research on directed percolation with long-range correlations in nonstabilizing random environments.

math.PR↗
arXiv2023

Towards Advanced Monitoring for Scientific Workflows

Scientific workflows consist of thousands of highly parallelized tasks executed in a distributed environment involving many components. Automatic tracing and investigation of the components' and tasks' performance metrics, traces, and behavior are necessary to support the end user with a level of abstraction since the large amount of data cannot be analyzed manually. The execution and monitoring of scientific workflows involves many components, the cluster infrastructure, its resource manager, the workflow, and the workflow tasks. All components in such an execution environment access different monitoring metrics and provide metrics on different abstraction levels. The combination and analysis of observed metrics from different components and their interdependencies are still widely unregarded. We specify four different monitoring layers that can serve as an architectural blueprint for the monitoring responsibilities and the interactions of components in the scientific workflow execution context. We describe the different monitoring metrics subject to the four layers and how the layers interact. Finally, we examine five state-of-the-art scientific workflow management systems (SWMS) in order to assess which steps are needed to enable our four-layer-based approach.

cs.DC↗
arXiv2023

Validity Constraints for Data Analysis Workflows

Porting a scientific data analysis workflow (DAW) to a cluster infrastructure, a new software stack, or even only a new dataset with some notably different properties is often challenging. Despite the structured definition of the steps (tasks) and their interdependencies during a complex data analysis in the DAW specification, relevant assumptions may remain unspecified and implicit. Such hidden assumptions often lead to crashing tasks without a reasonable error message, poor performance in general, non-terminating executions, or silent wrong results of the DAW, to name only a few possible consequences. Searching for the causes of such errors and drawbacks in a distributed compute cluster managed by a complex infrastructure stack, where DAWs for large datasets typically are executed, can be tedious and time-consuming. We propose validity constraints (VCs) as a new concept for DAW languages to alleviate this situation. A VC is a constraint specifying some logical conditions that must be fulfilled at certain times for DAW executions to be valid. When defined together with a DAW, VCs help to improve the portability, adaptability, and reusability of DAWs by making implicit assumptions explicit. Once specified, VC can be controlled automatically by the DAW infrastructure, and violations can lead to meaningful error messages and graceful behaviour (e.g., termination or invocation of repair mechanisms). We provide a broad list of possible VCs, classify them along multiple dimensions, and compare them to similar concepts one can find in related fields. We also provide a first sketch for VCs' implementation into existing DAW infrastructures.

cs.DC↗
arXiv2023

Continuum Percolation in a Nonstabilizing Environment

We prove phase transitions for continuum percolation in a Boolean model based on a Cox point process with nonstabilizing directing measure. The directing measure, which can be seen as a stationary random environment for the classical Poisson--Boolean model, is given by a planar rectangular Poisson line process. This Manhattan grid type construction features long-range dependencies in the environment, leading to absence of a sharp phase transition for the associated Cox--Boolean model. The phase transitions are established under individually as well as jointly varying parameters. Our proofs rest on discretization arguments and a comparison to percolation on randomly stretched lattices established in Hoffman 2005.

math.PR↗
arXiv2021

Stochastic Homogenization on Irregularly Perforated Domains

We study stochastic homogenization of a quasilinear parabolic PDE with nonlinear microscopic Robin conditions on a perforated domain. The focus of our work lies on the underlying geometry that does not allow standard homogenization techniques to be applied directly. Instead we prove homogenization on a regularized geometry and demonstrate afterwards that the form of the homogenized equation is independent from the regularization. Then we pass to the regularization limit to obtain the anticipated limit equation. Furthermore, we show that Boolean models of Poisson point processes are covered by our approach.

math.AP↗
arXiv2015

Anatomy and giant enhancement of the perpendicular magnetic anisotropy of cobalt-graphene heterostructures

We report strongly enhanced perpendicular magnetic anisotropy (PMA) of Co films by graphene coating from both first-principles and experiments. Our calculations show that graphene can dramatically boost the surface anisotropy of Co films up to twice the value of its pristine counterpart and can extend the out-of-plane effective anisotropy up to unprecedented thickness of 25~Å. These findings are supported by our experiments on graphene coating on Co films grown on Ir substrate. Furthermore, we report layer-resolved and orbital-hybridization-resolved anisotropy analysis which help understanding the physical mechanisms of PMA and more practically can help design structures with giant PMA. As an example, we propose super-exchange stabilized Co-graphene heterostructures with a robust out-of-plane constant effective PMA and linearly increasing interfacial anisotropy as a function of film thickness. These findings point towards possibilities to engineer graphene/ferromagnetic metal heterostructures with giant magnetic anisotropy more than 20 times larger compared to conventional multilayers, which constitutes a hallmark for future graphene and traditional spintronic technologies.

cond-mat.mtrl-sci↗