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On the Complexity of Universal Leader Election

Electing a leader is a fundamental task in distributed computing. In its implicit version, only the leader must know who is the elected leader. This paper focuses on studying the message and time complexity of randomized implicit leader election in synchronous distributed networks. Surprisingly, the most "obvious" complexity bounds have not been proven for randomized algorithms. The "obvious" lower bounds of O(m) messages (m is the number of edges in the network) and O(D) time (D is the network diameter) are non-trivial to show for randomized (Monte Carlo) algorithms. (Recent results that show that even O(n) (n is the number of nodes in the network) is not a lower bound on the messages in complete networks, make the above bounds somewhat less obvious). To the best of our knowledge, these basic lower bounds have not been established even for deterministic algorithms (except for the limited case of comparison algorithms, where it was also required that some nodes may not wake up spontaneously, and that D and n were not known).

We establish these fundamental lower bounds in this paper for the general case, even for randomized Monte Carlo algorithms. Our lower bounds are universal in the sense that they hold for all universal algorithms (such algorithms should work for all graphs), apply to every D, m, and n, and hold even if D, m, and n are known, all the nodes wake up simultaneously, and the algorithms can make anyuse of node's identities. To show that these bounds are tight, we present an O(m) messages algorithm. An O(D) time algorithm is known. A slight adaptation of our lower bound technique gives rise to an O(m) message lower bound for randomized broadcast algorithms.

An interesting fundamental problem is whether both upper bounds (messages and time) can be reached simultaneously in the randomized setting for all graphs. (The answer is known to be negative in the deterministic setting). We answer this problem partially by presenting a randomized algorithm that matches both complexities in some cases. This already separates (for some cases) randomized algorithms from deterministic ones. As first steps towards the general case, we present several universal leader election algorithms with bounds that trade-off messages versus time. We view our results as a step towards understanding the complexity of universal leader election in distributed networks.

Genome-wide association analysis identifies 13 new risk loci for schizophrenia

Schizophrenia is an idiopathic mental disorder with a heritable component and a substantial public health impact. We conducted a multi-stage genome-wide association study (GWAS) for schizophrenia beginning with a Swedish national sample (5,001 cases and 6,243 controls) followed by meta-analysis with previous schizophrenia GWAS (8,832 cases and 12,067 controls) and finally by replication of SNPs in 168 genomic regions in independent samples (7,413 cases, 19,762 controls and 581 parent-offspring trios). We identified 22 loci associated at genome-wide significance; 13 of these are new, and 1 was previously implicated in bipolar disorder. Examination of candidate genes at these loci suggests the involvement of neuronal calcium signaling. We estimate that 8,300 independent, mostly common SNPs (95% credible interval of 6,300-10,200 SNPs) contribute to risk for schizophrenia and that these collectively account for at least 32% of the variance in liability. Common genetic variation has an important role in the etiology of schizophrenia, and larger studies will allow more detailed understanding of this disorder.

Botanical travel, climate and David Moore’s moral geographies of Europe

During his forty-year curatorship of the Royal Dublin Society's botanical gardens in Glasnevin (1838–1879), David Moore undertook a number of excursions to continental Europe. These served to deepen the networks of plant exchange between Dublin and other botanical institutions and allowed him to examine the relationships between climate, plant survivability and societal development. This paper focuses on two trips taken in the 1860s to Scandinavia and Iberia and charts how Moore situated his experience of these places within a climatic hermeneutic. Moore's understanding of northern and southern Europe was organized around a set of judgments about their relative backwardness or advancement with respect to his experience of home and was seen through the lens of a moral climatology. Moreover, his Scots Presbyterian background and his commitment to natural theology informed his interpretation of the landscapes he encountered in his excursions across Europe.

Reconstructing apology: David Cameron's Bloody Sunday apology in the press

While there is an acknowledgement in apology research that political apologies are highly mediated, the process of mediation itself has lacked scrutiny. This article suggests that the idea of reconstruction helps to understand how apologies are mediated and evaluated. David Cameron's apology for Bloody Sunday is examined to see how he constructs four aspects of apology: social actors, consequences, categorization, and reasons. The reconstruction of those aspects by British, Unionist, and Nationalist press along with reconstructions made by soldiers in an online forum are considered. Data analysis was informed by thematic analysis and discourse analysis which helped to explore key aspects of reconstruction and how elements of Cameron's apology are altered in subsequent mediated forms of the apology. These mediated reconstructions of the apology allowed their authors to evaluate the apology in different ways. Thus, in this article, it is suggested that the evaluation of the apology by different groups is preceded by a reconstruction of it in accordance with rhetorical goals. This illuminates the process of mediation and helps to understand divergent responses to political apologies.