Consensus over Random Graph Processes: Network Borel-Cantelli Lemmas for Almost Sure Convergence

Distributed consensus computation over random graph processes is considered. The random graph process is defined as a sequence of random variables which take values from the set of all possible digraphs over the node set. At each time step, every node updates its state based on a Bernoulli trial, independent in time and among different nodes: either averaging among the neighbor set generated by the random graph, or sticking with its current state. Connectivity-independence and arc-independence are introduced to capture the fundamental influence of the random graphs on the consensus convergence. Necessary and/or sufficient conditions are presented on the success probabilities of the Bernoulli trials for the network to reach a global almost sure consensus, with some sharp threshold established revealing a consensus zero-one law. Convergence rates are established by lower and upper bounds of the $\epsilon$-computation time. We also generalize the concepts of connectivity/arc independence to their analogues from the $*$-mixing point of view, so that our results apply to a very wide class of graphical models, including the majority of random graph models in the literature, e.g., Erd\H{o}s-R\'{e}nyi, gossiping, and Markovian random graphs. We show that under $*$-mixing, our convergence analysis continues to hold and the corresponding almost sure consensus conditions are established. Finally, we further investigate almost sure finite-time convergence of random gossiping algorithms, and prove that the Bernoulli trials play a key role in ensuring finite-time convergence. These results add to the understanding of the interplay between random graphs, random computations, and convergence probability for distributed information processing.Comment: IEEE Transactions on Information Theory, In Pres

SCF Ensures Meiotic Chromosome Segregation Through a Resolution of Meiotic Recombination Intermediates

The SCF (Skp1-Cul1-F-box) complex contributes to a variety of cellular events including meiotic cell cycle control, but its function during meiosis is not understood well. Here we describe a novel function of SCF/Skp1 in meiotic recombination and subsequent chromosome segregation. The skp1 temperature-sensitive mutant exhibited abnormal distribution of spindle microtubules in meiosis II, which turned out to originate from abnormal bending of the spindle in meiosis I. Bent spindles were reported in mitosis of this mutant, but it remained unknown how SCF could affect spindle morphology. We found that the meiotic bent spindle in skp1 cells was due to a hypertension generated by chromosome entanglement. The spindle bending was suppressed by inhibiting double strand break (DSB) formation, indicating that the entanglement was generated by the meiotic recombination machinery. Consistently, Rhp51/Rad51-Rad22/Rad52 foci persisted until meiosis I in skp1 cells, proving accumulation of recombination intermediates. Intriguingly bent spindles were also observed in the mutant of Fbh1, an F-box protein containing the DNA helicase domain, which is involved in meiotic recombination. Genetic evidence suggested its cooperation with SCF/Skp1. Thus, SCF/Skp1 together with Fbh1 is likely to function in the resolution of meiotic recombination intermediates, thereby ensuring proper chromosome segregation

Fission Yeast Tel1ATM and Rad3ATR Promote Telomere Protection and Telomerase Recruitment

The checkpoint kinases ATM and ATR are redundantly required for maintenance of stable telomeres in diverse organisms, including budding and fission yeasts, Arabidopsis, Drosophila, and mammals. However, the molecular basis for telomere instability in cells lacking ATM and ATR has not yet been elucidated fully in organisms that utilize both the telomere protection complex shelterin and telomerase to maintain telomeres, such as fission yeast and humans. Here, we demonstrate by quantitative chromatin immunoprecipitation (ChIP) assays that simultaneous loss of Tel1ATM and Rad3ATR kinases leads to a defect in recruitment of telomerase to telomeres, reduced binding of the shelterin complex subunits Ccq1 and Tpz1, and increased binding of RPA and homologous recombination repair factors to telomeres. Moreover, we show that interaction between Tpz1-Ccq1 and telomerase, thought to be important for telomerase recruitment to telomeres, is disrupted in tel1Δ rad3Δ cells. Thus, Tel1ATM and Rad3ATR are redundantly required for both protection of telomeres against recombination and promotion of telomerase recruitment. Based on our current findings, we propose the existence of a regulatory loop between Tel1ATM/Rad3ATR kinases and Tpz1-Ccq1 to ensure proper protection and maintenance of telomeres in fission yeast

Rad51 Inhibits Translocation Formation by Non-Conservative Homologous Recombination in Saccharomyces cerevisiae

Chromosomal translocations are a primary biological response to ionizing radiation (IR) exposure, and are likely to result from the inappropriate repair of the DNA double-strand breaks (DSBs) that are created. An abundance of repetitive sequences in eukaryotic genomes provides ample opportunity for such breaks to be repaired by homologous recombination (HR) between non-allelic repeats. Interestingly, in the budding yeast, Saccharomyces cerevisiae the central strand exchange protein, Rad51 that is required for DSB repair by gene conversion between unlinked repeats that conserves genomic structure also suppresses translocation formation by several HR mechanisms. In particular, Rad51 suppresses translocation formation by single-strand annealing (SSA), perhaps the most efficient mechanism for translocation formation by HR in both yeast and mammalian cells. Further, the enhanced translocation formation that emerges in the absence of Rad51 displays a distinct pattern of genetic control, suggesting that this occurs by a separate mechanism. Since hypomorphic mutations in RAD51 in mammalian cells also reduce DSB repair by conservative gene conversion and stimulate non-conservative repair by SSA, this mechanism may also operate in humans and, perhaps contribute to the genome instability that propels the development of cancer

Psychometric Properties of the Parent and Teacher Versions of the Strengths and Difficulties Questionnaire for 4- to 12-Year-Olds: A Review

Since its development, the Strengths and Difficulties Questionnaire (SDQ) has been widely used in both research and practice. The SDQ screens for positive and negative psychological attributes. This review aims to provide an overview of the psychometric properties of the SDQ for 4- to 12-year-olds. Results from 48 studies (N = 131,223) on reliability and validity of the parent and teacher SDQ are summarized quantitatively and descriptively. Internal consistency, test–retest reliability, and inter-rater agreement are satisfactory for the parent and teacher versions. At subscale level, the reliability of the teacher version seemed stronger compared to that of the parent version. Concerning validity, 15 out of 18 studies confirmed the five-factor structure. Correlations with other measures of psychopathology as well as the screening ability of the SDQ are sufficient. This review shows that the psychometric properties of the SDQ are strong, particularly for the teacher version. For practice, this implies that the use of the SDQ as a screening instrument should be continued. Longitudinal research studies should investigate predictive validity. For both practice and research, we emphasize the use of a multi-informant approach