Dynamic and Multi-functional Labeling Schemes

We investigate labeling schemes supporting adjacency, ancestry, sibling, and connectivity queries in forests. In the course of more than 20 years, the existence of $\log n + O(\log \log)$ labeling schemes supporting each of these functions was proven, with the most recent being ancestry [Fraigniaud and Korman, STOC '10]. Several multi-functional labeling schemes also enjoy lower or upper bounds of $\log n + \Omega(\log \log n)$ or $\log n + O(\log \log n)$ respectively. Notably an upper bound of $\log n + 5\log \log n$ for adjacency+siblings and a lower bound of $\log n + \log \log n$ for each of the functions siblings, ancestry, and connectivity [Alstrup et al., SODA '03]. We improve the constants hidden in the $O$-notation. In particular we show a $\log n + 2\log \log n$ lower bound for connectivity+ancestry and connectivity+siblings, as well as an upper bound of $\log n + 3\log \log n + O(\log \log \log n)$ for connectivity+adjacency+siblings by altering existing methods. In the context of dynamic labeling schemes it is known that ancestry requires $\Omega(n)$ bits [Cohen, et al. PODS '02]. In contrast, we show upper and lower bounds on the label size for adjacency, siblings, and connectivity of $2\log n$ bits, and $3 \log n$ to support all three functions. There exist efficient adjacency labeling schemes for planar, bounded treewidth, bounded arboricity and interval graphs. In a dynamic setting, we show a lower bound of $\Omega(n)$ for each of those families.Comment: 17 pages, 5 figure

How Long It Takes for an Ordinary Node with an Ordinary ID to Output?

In the context of distributed synchronous computing, processors perform in rounds, and the time-complexity of a distributed algorithm is classically defined as the number of rounds before all computing nodes have output. Hence, this complexity measure captures the running time of the slowest node(s). In this paper, we are interested in the running time of the ordinary nodes, to be compared with the running time of the slowest nodes. The node-averaged time-complexity of a distributed algorithm on a given instance is defined as the average, taken over every node of the instance, of the number of rounds before that node output. We compare the node-averaged time-complexity with the classical one in the standard LOCAL model for distributed network computing. We show that there can be an exponential gap between the node-averaged time-complexity and the classical time-complexity, as witnessed by, e.g., leader election. Our first main result is a positive one, stating that, in fact, the two time-complexities behave the same for a large class of problems on very sparse graphs. In particular, we show that, for LCL problems on cycles, the node-averaged time complexity is of the same order of magnitude as the slowest node time-complexity. In addition, in the LOCAL model, the time-complexity is computed as a worst case over all possible identity assignments to the nodes of the network. In this paper, we also investigate the ID-averaged time-complexity, when the number of rounds is averaged over all possible identity assignments. Our second main result is that the ID-averaged time-complexity is essentially the same as the expected time-complexity of randomized algorithms (where the expectation is taken over all possible random bits used by the nodes, and the number of rounds is measured for the worst-case identity assignment). Finally, we study the node-averaged ID-averaged time-complexity.Comment: (Submitted) Journal versio

Labeling Schemes for Bounded Degree Graphs

We investigate adjacency labeling schemes for graphs of bounded degree $\Delta = O(1)$. In particular, we present an optimal (up to an additive constant) $\log n + O(1)$ adjacency labeling scheme for bounded degree trees. The latter scheme is derived from a labeling scheme for bounded degree outerplanar graphs. Our results complement a similar bound recently obtained for bounded depth trees [Fraigniaud and Korman, SODA 10], and may provide new insights for closing the long standing gap for adjacency in trees [Alstrup and Rauhe, FOCS 02]. We also provide improved labeling schemes for bounded degree planar graphs. Finally, we use combinatorial number systems and present an improved adjacency labeling schemes for graphs of bounded degree $\Delta$ with $(e+1)\sqrt{n} < \Delta \leq n/5$

Influenza epidemiology, vaccine coverage and vaccine effectiveness in sentinel Australian hospitals in 2013: the Influenza Complications Alert Network

The National Influenza Program aims to reduce serious morbidity and mortality from influenza by providing public funding for vaccination to at-risk groups. The Influenza Complications Alert Network (FluCAN) is a sentinel hospital-based surveillance program that operates at 14 sites in all states and territories in Australia. This report summarises the epidemiology of hospitalisations with confirmed influenza, estimates vaccine coverage and influenza vaccine protection against hospitalisation with influenza during the 2013 influenza season. In this observational study, cases were defined as patients admitted to one of the sentinel hospitals, with influenza confirmed by nucleic acid testing. Controls were patients who had acute respiratory illnesses who were test-negative for influenza. Vaccine effectiveness was estimated as 1 minus the odds ratio of vaccination in case patients compared with control patients, after adjusting for known confounders. During the period 5 April to 31 October 2012, 631 patients were admitted with confirmed influenza at the 14 FluCAN sentinel hospitals. Of these, 31% were more than 65 years of age, 9.5% were Indigenous Australians, 4.3% were pregnant and 77% had chronic co-morbidities. Influenza B was detected in 30% of patients. Vaccination coverage was estimated at 81% in patients more than 65 years of age but only 49% in patients aged less than 65 years with chronic comorbidities. Vaccination effectiveness against hospitalisation with influenza was estimated at 50% (95% confidence interval: 33%, 63%, P<0.001). We detected a significant number of hospital admissions with confirmed influenza in a national observational study. Vaccine coverage was incomplete in at-risk groups, particularly non-elderly patients with medical comorbidities. Our results suggest that the seasonal influenza vaccine was moderately protective against hospitalisation with influenza in the 2013 season. This work i

ADHD 24/7:Circadian clock genes, chronotherapy and sleep/wake cycle insufficiencies in ADHD

Objectives: The current paper addresses the evidence for circadian clock characteristics associated with attention-deficit hyperactivity disorder (ADHD), and possible therapeutic approaches based on chronomodulation through bright light (BL) therapy. Methods: We review the data reported in ADHD on genetic risk factors for phase-delayed circadian rhythms and on the role of photic input in circadian re-alignment. Results: Single nucleotide polymorphisms in circadian genes were recently associated with core ADHD symptoms, increased evening-orientation and frequent sleep problems. Additionally, alterations in exposure and response to photic input may underlie circadian problems in ADHD. BL therapy was shown to be effective for re-alignment of circadian physiology toward morningness, reducing sleep disturbances and bringing overall improvement in ADHD symptoms. The susceptibility of the circadian system to phase shift by timed BL exposure may have broad cost-effective potential implications for the treatment of ADHD. Conclusions: We conclude that further research of circadian function in ADHD should focus on detection of genetic markers (e.g., using human skin fibroblasts) and development of BL-based therapeutic interventions

Influenza Vaccine Effectiveness against Hospitalisation with Confirmed Influenza in the 2010-11 Seasons: A Test-negative Observational Study

Immunisation programs are designed to reduce serious morbidity and mortality from influenza, but most evidence supporting the effectiveness of this intervention has focused on disease in the community or in primary care settings. We aimed to examine the effectiveness of influenza vaccination against hospitalisation with confirmed influenza. We compared influenza vaccination status in patients hospitalised with PCR-confirmed influenza with patients hospitalised with influenza-negative respiratory infections in an Australian sentinel surveillance system. Vaccine effectiveness was estimated from the odds ratio of vaccination in cases and controls. We performed both simple multivariate regression and a stratified analysis based on propensity score of vaccination. Vaccination status was ascertained in 333 of 598 patients with confirmed influenza and 785 of 1384 test-negative patients. Overall estimated crude vaccine effectiveness was 57% (41%, 68%). After adjusting for age, chronic comorbidities and pregnancy status, the estimated vaccine effectiveness was 37% (95% CI: 12%, 55%). In an analysis accounting for a propensity score for vaccination, the estimated vaccine effectiveness was 48.3% (95% CI: 30.0, 61.8%). Influenza vaccination was moderately protective against hospitalisation with influenza in the 2010 and 2011 seasons

Hyperbolic Geometry of Complex Networks

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as non-interacting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure