Pattern Matching in Multiple Streams

We investigate the problem of deterministic pattern matching in multiple streams. In this model, one symbol arrives at a time and is associated with one of s streaming texts. The task at each time step is to report if there is a new match between a fixed pattern of length m and a newly updated stream. As is usual in the streaming context, the goal is to use as little space as possible while still reporting matches quickly. We give almost matching upper and lower space bounds for three distinct pattern matching problems. For exact matching we show that the problem can be solved in constant time per arriving symbol and O(m+s) words of space. For the k-mismatch and k-difference problems we give O(k) time solutions that require O(m+ks) words of space. In all three cases we also give space lower bounds which show our methods are optimal up to a single logarithmic factor. Finally we set out a number of open problems related to this new model for pattern matching.Comment: 13 pages, 1 figur

Nonlocal Astroparticles in Einstein's Universe

Gravitational probes should maintain spatial flatness for Einsten-Infeld-Hoffmann dynamics of relativistic matter-energy. The continuous elementary source/particle in Einstein's gravitational theory is the r^{-4} radial energy density rather than the delta-operator density in empty-space gravitation. The space energy integral of such an infinite (astro)particle is finite and determines its nonlocal gravitational charge for the energy-to-energy attraction of other nonlocal (astro)particles. The non-empty flat space of the undivided material Universe is charged continuously by the world energy density of the global ensemble of overlapping radial particles. Nonlocal gravitational/inertial energy-charges incorporate Machian relativism quantitatively into Einstein's gravitation for self-contained SR-GR dynamics without references on Newton's mass-to-mass attraction.Comment: 9 pages, typos and arguments adde

Variation in incentive effects across neighbourhoods:An example from the Irish Longitudinal Study of ageing

Small monetary incentives increase survey cooperation rates, however evidence suggests that the appeal of incentives may vary across sample subgroups. Fieldwork budgets can be most effectively distributed by targeting those subgroups where incentives will have the strongest appeal. We examine data from a randomised experiment implemented in the pilot phase of the Irish Longitudinal Study of Ageing, which randomly assigned households to receive a higher (€25) or lower (€10) incentive amount. Using a random effects logistic regression model, we observe a variable effect of the higher incentive across geographic neighbourhoods. The higher incentive has the largest impact in neighbourhoods where baseline cooperation is low, as predicted by Leverage-Saliency theory. Auxiliary neighbourhood-level variables are linked to the sample frame to explore this variation further, however none of these moderate the incentive effect, suggesting that richer information is needed to identify sample subgroups where incentive budgets should be directed