Jakob Gulddahl Rasmussen

Perfect simulation of Hawkes processes

Our objective is to construct a perfect simulation algorithm for unmarked and marked Hawkes processes. The usual straightforward simulation algorithm suffers from edge effects, whereas our perfect simulation algorithm does not. By viewing Hawkes processes as Poisson cluster processes and using their branching and conditional independence structures, useful approximations of the distribution function for the length of a cluster are derived. This is used to construct upper and lower processes for the perfect simulation algorithm. A tail-lightness condition turns out to be of importance for the applicability of the perfect simulation algorithm. Examples of applications and empirical results are presented.

Spatial-Temporal Modeling of Forest Gaps Generated by Colonization From Below- and Above-Ground Bark Beetle Species

Studies of forest declines are important, because they both reduce timber production and affect successional trajectories of landscapes and ecosystems. Of particular interest is the decline of red pines, which is characterized by expanding areas of dead and chlorotic trees in plantations throughout the Great Lakes region. Here we examine the impact of two bark beetle groups, red turpentine beetles and pine engraver bark beetles, on tree mortality and the subsequent gap formation over time in a plantation in Wisconsin. We construct spatial-temporal statistical models that quantify the relations among red turpentine beetle colonization, pine engraver bark beetle colonization, and mortality of red pine trees while accounting for correlation across space and over time. We extend traditional Markov random-field models to include temporal terms and multiple-response variables aimed at developing a suitable set of statistical models for addressing the scientific questions about the forest ecosystem under study. For statistical inference, we adopt a Bayesian hierarchical modeling approach and devise Markov chain Monte Carlo algorithms for obtaining the posterior distributions of model parameters as well as posterior predictive distributions. In particular, we implement path sampling combined with perfect simulation for autologistic models while formally addressing the posterior propriety under an improper uniform prior. Our data analysis results suggest that red turpentine beetle colonization is associated with a higher likelihood of pine engraver bark beetle colonization and that pine engraver bark beetle colonization is associated with higher likelihood of red pine tree mortality, whereas there is no direct association between red turpentine beetle colonization and red pine tree mortality. There is strong evidence that red turpentine beetle colonization does not kill a red pine tree directly, but rather predisposes the tree to subsequent colonization by pine engraver bark beetles. The evidence is also strong that pine engraver bark beetles are the ultimate mortality agents of red pine trees.

Connectivity analysis of one-dimensional ad-hoc networks

Application and communication protocols in dynamic ad-hoc networks are exposed to physical limitations imposed by the connectivity relations that result from mobility. Motivated by vehicular freeway scenarios, this paper analyzes a number of important connectivity metrics for instantaneous snapshots of stochastic geographic movement patterns: (1) The single-hop connectivity number, corresponding to the number of single-hop neighbors of a mobile node; (2) the multi-hop connectivity number, expressing the number of nodes reachable via multi-hop paths of arbitrary hop-count; (3) the connectivity distance, expressing the geographic distance that a message can be propagated in the network on multi-hop paths; (4) the connectivity hops, which corresponds to the number of hops that are necessary to reach all nodes in the connected network. The paper develops analytic expressions for the distributions and moments of these random variables for general stationary MAP processes on a one dimensional space. The numerical results compare bursty vehicular traffic with independent movement scenarios described by a Poisson process, illustrate in examples the impact of a random communication range, and demonstrate the usefulness of MAP processes via comparison with vehicular simulation traces.

Connectivity dynamics in vehicular freeway scenarios

Vehicular ad-hoc networks have received increasing interest in the last years for their potential to support a variety of services and applications in order to improve driving safety or traffic efficiency and to provide information and entertainment to the users. This paper focuses on the analysis of some connectivity characteristics in dynamic vehicular communication scenarios, that are important for the design and the performance and dependability assessment of such applications. In particular, we focus on the process describing the occurrence of encounters between cars in single and multi-hop scenarios. Using analytical proofs and simulation experiments, it is shown that under some key assumptions on the movements and the placement of the cars, this process can be approximated as a stationary or a nonhomogeneous Poisson process. Results are also provided concerning the duration of connections in the ad-hoc domain.

Detection and spatial characterization of minicolumnarity in the human cerebral cortex.

Spatial characterization of vertical organization of neurons in human cerebral cortex, cortical columnarity or minicolumns, and its possible association with various psychiatric and neurological diseases has been investigated for many years.

Analysis of Information Quality in Event Triggered Smart Grid Control

The integration of renewable energy sources into the power grid requires added control intelligence which imposes new communication requirements onto the future power grid. Since large scale implementation of new communication infrastructure is infeasible, we consider methods of increasing dependability of existing networks. We develop models for network delays and information dynamics, and uses these to model information quality for three given information access schemes in an event triggered control scenario. We analyse the impact of model parameters, and show how optimal choice of information access scheme depends on network conditions as well as trade-offs between information quality, network resources and control reactivity.

A class of stochastic hybrid systems with state-dependent switching noise

In this paper, we develop theoretical results based on a proposed method for modeling switching noise for a class of hybrid systems with piecewise linear partitioned state space, and state-depending switching. We devise a stochastic model of such systems, whose global dynamics is governed by a continuous-time stochastic process. The main result of this paper is that we may identify the realizations of the global dynamics with the solutions of a differential inclusion. Hence, an analysis of switched systems with switching noise can be carried out either based on a non-deterministic method via the differential inclusion, or on a stochastic method via the stochastic process. Furthermore, we describe how to construct intensity plots, which provide a quick overview of the behavior of the system. An example is included to illustrate this.

Spatial cluster point processes related to Poisson-Voronoi tessellations

We discuss how to construct models for cluster point processes within ‘territories’ modelled by

Service Degradation in Context Management Frameworks

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