41 research outputs found

    Connectivity Thresholds for Bounded Size Rules

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    In an Achlioptas process, starting with a graph that has n vertices and no edge, in each round d1d \geq 1 edges are drawn uniformly at random, and using some rule exactly one of them is chosen and added to the evolving graph. For the class of Achlioptas processes we investigate how much impact the rule has on one of the most basic properties of a graph: connectivity. Our main results are twofold. First, we study the prominent class of bounded size rules, which select the edge to add according to the component sizes of its vertices, treating all sizes larger than some constant equally. For such rules we provide a fine analysis that exposes the limiting distribution of the number of rounds until the graph gets connected, and we give a detailed picture of the dynamics of the formation of the single component from smaller components. Second, our results allow us to study the connectivity transition of all Achlioptas processes, in the sense that we identify a process that accelerates it as much as possible

    Measurement equivalence in probability and nonprobability online panels

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    Nonprobability online panels are commonly used in the social sciences as a fast and inexpensive way of collecting data in contrast to more expensive probability-based panels. Given their ubiquitous use in social science research, a great deal of research is being undertaken to assess the properties of nonprobability panels relative to probability ones. Much of this research focuses on selection bias, however, there is considerably less research assessing the comparability (or equivalence) of measurements collected from respondents in nonprobability and probability panels. This article contributes to addressing this research gap by testing whether measurement equivalence holds between multiple probability and nonprobability online panels in Australia and Germany. Using equivalence testing in the Confirmatory Factor Analysis framework, we assessed measurement equivalence in six multi-item scales (three in each country). We found significant measurement differences between probability and nonprobability panels and within them, even after weighting by demographic variables. These results suggest that combining or comparing multi-item scale data from different sources should be done with caution. We conclude with a discussion of the possible causes of these findings, their implications for survey research, and some guidance for data users.publishedVersio

    The linear hidden subset problem for the (1+1) EA with scheduled and adaptive mutation rates

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    We study unbiased (1+1)(1+1) evolutionary algorithms on linear functions with an unknown number nn of bits with non-zero weight. Static algorithms achieve an optimal runtime of O(n(lnn)2+ϵ)O(n (\ln n)^{2+\epsilon}), however, it remained unclear whether more dynamic parameter policies could yield better runtime guarantees. We consider two setups: one where the mutation rate follows a fixed schedule, and one where it may be adapted depending on the history of the run. For the first setup, we give a schedule that achieves a runtime of (1±o(1))βnlnn(1\pm o(1))\beta n \ln n, where β3.552\beta \approx 3.552, which is an asymptotic improvement over the runtime of the static setup. Moreover, we show that no schedule admits a better runtime guarantee and that the optimal schedule is essentially unique. For the second setup, we show that the runtime can be further improved to (1±o(1))enlnn(1\pm o(1)) e n \ln n, which matches the performance of algorithms that know nn in advance. Finally, we study the related model of initial segment uncertainty with static position-dependent mutation rates, and derive asymptotically optimal lower bounds. This answers a question by Doerr, Doerr, and K\"otzing

    A Hippocampal Model for Behavioral Time Acquisition and Fast Bidirectional Replay of Spatio-Temporal Memory Sequences

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    The hippocampus is known to play a crucial role in the formation of long-term memory. For this, fast replays of previously experienced activities during sleep or after reward experiences are believed to be crucial. But how such replays are generated is still completely unclear. In this paper we propose a possible mechanism for this: we present a model that can store experienced trajectories on a behavioral timescale after a single run, and can subsequently bidirectionally replay such trajectories, thereby omitting any specifics of the previous behavior like speed, etc, but allowing repetitions of events, even with different subsequent events. Our solution builds on well-known concepts, one-shot learning and synfire chains, enhancing them by additional mechanisms using global inhibition and disinhibition. For replays our approach relies on dendritic spikes and cholinergic modulation, as supported by experimental data. We also hypothesize a functional role of disinhibition as a pacemaker during behavioral time

    Abstractive Text Summarization for Icelandic

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