Random Times for Markov Processes with Killing

We consider random time changes in Markov processes with killing potentials. We study how random time changes may be introduced in these Markov processes with killing potential and how these changes may influence their time behavior. As applications, we study the parabolic Anderson problem, the non-local Schrödinger operators as well as the generalized Anderson problem.

Probing Many-Body Systems Near Spectral Degeneracies

The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying part. This separation is strongly affected when spectral degeneracies occur, for instance, in the presence of spontaneous symmetry breaking. Moreover, the slowest decay rate is determined by the smallest energy level spacing, and this decay rate diverges at the spectral degeneracies. Probing the quantum evolution with the diagonal elements of the time correlation matrix is discussed as a general concept and tested in the case of a bosonic Josephson junction. It reveals for the latter characteristic properties at the transition to Hilbert-space localization.

Non-Parametric Stochastic Sequential Assignment With Random Arrival Times

We consider a problem wherein jobs arrive at random times and assume random values. Upon each job arrival, the decision-maker must decide immediately whether or not to accept the job and gain the value on offer as a reward, with the constraint that they may only accept at most n jobs over some reference time period. The decision-maker only has access to M independent realisations of the job arrival process. We propose an algorithm, Non-Parametric Sequential Allocation (NPSA), for solving this problem. Moreover, we prove that the expected reward returned by the NPSA algorithm converges in probability to optimality as M grows large. We demonstrate the effectiveness of the algorithm empirically on synthetic data and on public fraud-detection datasets, from where the motivation for this work is derived.

Situation Awareness Adaptive Alerting in an Aircraft Cockpit: A Simulator Study

The goal of this study was to develop an automated cockpit support system that is adaptive to the flight crew’s situation awareness (SA) estimated by online gaze analysis. Flight crew errors are often attributed to low SA. Online measurement of SA could be used to automatically guide the user’s attention for the sake of fewer errors and better performance.An eye-tracking based measure for SA was developed and used for the adaptive generation of alerts in a flight simulator. In an experiment, ten certified pilots conducted two trials with no and adaptive alerting. The experimental task involved tracking of flight parameters which were partially disturbed or changed at random times. Our online estimation of SA showed a strong correlation with observed pilot performance. With adaptive alerts, the average performance increased in those experimental tasks, where a situational change could not be predicted by participants. Also, adaptive alerts improved change detection and reduced the number of outliers, where a change was not noticed for an exceptionally long time. However, subjective rating was poor due to low transparency and false positives. SA-adaptive support can improve change detection performance in typical tasks on the flight deck. For a greater acceptance, pilots should be trained to understand the adaption policy.

A Semi-Deterministic Random Walk with Resetting

We consider a discrete-time random walk (xt) which, at random times, is reset to the starting position and performs a deterministic motion between them. We show that the quantity Prxt+1=n+1|xt=n,n→∞ determines if the system is averse, neutral or inclined towards resetting. It also classifies the stationary distribution. Double barrier probabilities, first passage times and the distribution of the escape time from intervals are determined.

Formation and inter-piconet communications in cognitive personal area networks

This dissertation presents a new approach for achieving group rendezvous with a coordinator node towards forming a Cognitive Personal Area Network (CPAN) by an arbitrary number of nodes. We propose a protocol for the time to form CPAN in which the nodes join the coordinator simultaneously instead of sequentially. Specifically, we develop an analytical model and derive the distribution of time to form CPAN under the considerations of random arrivals of nodes and their random times to rendezvous with coordinator. We also investigate the CPAN formation time by considering the random activity of primary user (PU). Besides operating in a CPAN, the nodes may have traffic destined to the nodes of other CPAN. In this dissertation, we also propose a bridging protocol in which a shared (bridge) node routes the inter-CPAN traffic between two CPANs. As the bridge node shares its time between two CPANs, the bridge traffic gets priority over that of ordinary nodes in both CPANs. We consider a single, unidirectional bridge because the traffic in the opposite direction can easily be accommodated by having another bridge node. We develop an analytical model based on probabilistic modeling and queueing theory to evaluate the performance of the bridging protocol. We validate the network performance by analyzing the waiting time of local and non-local packets and how the node or bridge transmission is affected by the collision with primary source activity. Finally, we propose a low-overhead two-way bridging scheme for two-hop CPANs, which is more realistic and can be used a basis for routing inter-CPAN traffic in a multihop network. In this advance bringing protocol, the bridge switches between the CPANs without any predefined arrangement, which resulted in simplified bridge scheduling and increased fairness for all nodes. We also analyze its performance through probabilistic analysis and renewal theory. We show that the CPANs are indeed decoupled in terms of synchronization, however the performance of both local and non-local traffic in either CPAN depends on the traffic intensity in both CPANs as well as on the portion of traffic targeting non-local destinations

Formation and inter-piconet communications in cognitive personal area networks

This dissertation presents a new approach for achieving group rendezvous with a coordinator node towards forming a Cognitive Personal Area Network (CPAN) by an arbitrary number of nodes. We propose a protocol for the time to form CPAN in which the nodes join the coordinator simultaneously instead of sequentially. Specifically, we develop an analytical model and derive the distribution of time to form CPAN under the considerations of random arrivals of nodes and their random times to rendezvous with coordinator. We also investigate the CPAN formation time by considering the random activity of primary user (PU). Besides operating in a CPAN, the nodes may have traffic destined to the nodes of other CPAN. In this dissertation, we also propose a bridging protocol in which a shared (bridge) node routes the inter-CPAN traffic between two CPANs. As the bridge node shares its time between two CPANs, the bridge traffic gets priority over that of ordinary nodes in both CPANs. We consider a single, unidirectional bridge because the traffic in the opposite direction can easily be accommodated by having another bridge node. We develop an analytical model based on probabilistic modeling and queueing theory to evaluate the performance of the bridging protocol. We validate the network performance by analyzing the waiting time of local and non-local packets and how the node or bridge transmission is affected by the collision with primary source activity. Finally, we propose a low-overhead two-way bridging scheme for two-hop CPANs, which is more realistic and can be used a basis for routing inter-CPAN traffic in a multihop network. In this advance bringing protocol, the bridge switches between the CPANs without any predefined arrangement, which resulted in simplified bridge scheduling and increased fairness for all nodes. We also analyze its performance through probabilistic analysis and renewal theory. We show that the CPANs are indeed decoupled in terms of synchronization, however the performance of both local and non-local traffic in either CPAN depends on the traffic intensity in both CPANs as well as on the portion of traffic targeting non-local destinations

Predicting partially observed processes on temporal networks by Dynamics-Aware Node Embeddings (DyANE)

Low-dimensional vector representations of network nodes have proven successful to feed graph data to machine learning algorithms and to improve performance across diverse tasks. Most of the embedding techniques, however, have been developed with the goal of achieving dense, low-dimensional encoding of network structure and patterns. Here, we present a node embedding technique aimed at providing low-dimensional feature vectors that are informative of dynamical processes occurring over temporal networks – rather than of the network structure itself – with the goal of enabling prediction tasks related to the evolution and outcome of these processes. We achieve this by using a lossless modified supra-adjacency representation of temporal networks and building on standard embedding techniques for static graphs based on random walks. We show that the resulting embedding vectors are useful for prediction tasks related to paradigmatic dynamical processes, namely epidemic spreading over empirical temporal networks. In particular, we illustrate the performance of our approach for the prediction of nodes’ epidemic states in single instances of a spreading process. We show how framing this task as a supervised multi-label classification task on the embedding vectors allows us to estimate the temporal evolution of the entire system from a partial sampling of nodes at random times, with potential impact for nowcasting infectious disease dynamics.