Extremal Aging For Trap Models

In the seminal work [5], Ben Arous and \v{C}ern\'y give a general characterization of aging for trap models in terms of $\alpha$-stable subordinators with $\alpha \in (0,1)$. Some of the important examples that fall into this universality class are Random Hopping Time (RHT) dynamics of Random Energy Model (REM) and $p$-spin models observed on exponential time scales. In this paper, we explain a different aging mechanism in terms of {\it extremal processes} that can be seen as the extension of $\alpha$-stable aging to the case $\alpha=0$. We apply this mechanism to the RHT dynamics of the REM for a wide range of temperature and time scales. The other examples that exhibit extremal aging include the Sherrington Kirkpatrick (SK) model and $p$-spin models [6, 9], and biased random walk on critical Galton-Watson trees conditioned to survive [11]

Uneven key pre-distribution scheme for multi-phase wireless sensor networks

In multi-phase Wireless Sensor Networks (WSNs), sensor nodes are redeployed periodically to replace nodes whose batteries are depleted. In order to keep the network resilient against node capture attacks across different deployment epochs, called generations, it is necessary to refresh the key pools from which cryptographic keys are distributed. In this paper, we propose Uneven Key Pre-distribution (UKP) scheme that uses multiple different key pools at each generation. Our UKP scheme provides self healing that improves the resiliency of the network at a higher level as compared to an existing scheme in the literature. Moreover, our scheme provides perfect local and global connectivity. We conduct our simulations in mobile environment to see how our scheme performs under more realistic scenarios

On the Wiener disorder problem

In the Wiener disorder problem, the drift of a Wiener process changes suddenly at some unknown and unobservable disorder time. The objective is to detect this change as quickly as possible after it happens. Earlier work on the Bayesian formulation of this problem brings optimal (or asymptotically optimal) detection rules assuming that the prior distribution of the change time is given at time zero, and additional information is received by observing the Wiener process only. Here, we consider a different information structure where possible causes of this disorder are observed. More precisely, we assume that we also observe an arrival/counting process representing external shocks. The disorder happens because of these shocks, and the change time coincides with one of the arrival times. Such a formulation arises, for example, from detecting a change in financial data caused by major financial events, or detecting damages in structures caused by earthquakes. In this paper, we formulate the problem in a Bayesian framework assuming that those observable shocks form a Poisson process. We present an optimal detection rule that minimizes a linear Bayes risk, which includes the expected detection delay and the probability of early false alarms. We also give the solution of the ``variational formulation'' where the objective is to minimize the detection delay over all stopping rules for which the false alarm probability does not exceed a given constant.Comment: Published in at http://dx.doi.org/10.1214/09-AAP655 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org