Succinct Representations of Permutations and Functions

We investigate the problem of succinctly representing an arbitrary permutation, \pi, on {0,...,n-1} so that \pi^k(i) can be computed quickly for any i and any (positive or negative) integer power k. A representation taking (1+\epsilon) n lg n + O(1) bits suffices to compute arbitrary powers in constant time, for any positive constant \epsilon <= 1. A representation taking the optimal \ceil{\lg n!} + o(n) bits can be used to compute arbitrary powers in O(lg n / lg lg n) time. We then consider the more general problem of succinctly representing an arbitrary function, f: [n] \rightarrow [n] so that f^k(i) can be computed quickly for any i and any integer power k. We give a representation that takes (1+\epsilon) n lg n + O(1) bits, for any positive constant \epsilon <= 1, and computes arbitrary positive powers in constant time. It can also be used to compute f^k(i), for any negative integer k, in optimal O(1+|f^k(i)|) time. We place emphasis on the redundancy, or the space beyond the information-theoretic lower bound that the data structure uses in order to support operations efficiently. A number of lower bounds have recently been shown on the redundancy of data structures. These lower bounds confirm the space-time optimality of some of our solutions. Furthermore, the redundancy of one of our structures "surpasses" a recent lower bound by Golynski [Golynski, SODA 2009], thus demonstrating the limitations of this lower bound.Comment: Preliminary versions of these results have appeared in the Proceedings of ICALP 2003 and 2004. However, all results in this version are improved over the earlier conference versio

Explicit deterministic constructions for membership in the bitprobe model

We look at time-space tradeoffs for the static membership problem in the bit-probe model. The problem is to represent a set of size up to n from a universe of size m using a small number of bits so that given an element of the universe, its membership in the set can be determined with as few bit probes to the representation as possible. We show several deterministic upper bounds for the case when the number of bit probes, is small, by explicit constructions, culminating in one that uses o(m) bits of space where membership can be determined with [lg lgn] + 2 adaptive bit probes. We also show two tight lower bounds on space for a restricted two probe adaptive scheme

More Haste, Less Waste: Lowering the Redundancy in Fully Indexable Dictionaries

We consider the problem of representing, in a compressed format, a bit-vector $S$ of $m$ bits with $n$ 1s, supporting the following operations, where $b \in \{0, 1 \}$: $rank_b(S,i)$ returns the number of occurrences of bit $b$ in the prefix $S[1..i]$; $select_b(S,i)$ returns the position of the $i$th occurrence of bit $b$ in $S$. Such a data structure is called \emph{fully indexable dictionary (FID)} [Raman et al.,2007], and is at least as powerful as predecessor data structures. Our focus is on space-efficient FIDs on the \textsc{ram} model with word size $\Theta(\lg m)$ and constant time for all operations, so that the time cost is independent of the input size. Given the bitstring $S$ to be encoded, having length $m$ and containing $n$ ones, the minimal amount of information that needs to be stored is $B(n,m) = \lceil \log {{m}\choose{n}} \rceil$. The state of the art in building a FID for $S$ is given in [Patrascu,2008] using $B(m,n)+O(m / ((\log m/ t) ^t)) + O(m^{3/4})$ bits, to support the operations in $O(t)$ time. Here, we propose a parametric data structure exhibiting a time/space trade-off such that, for any real constants $0 0$, it uses B(n,m) + O(n^{1+\delta} + n (\frac{m}{n^s})^\eps) bits and performs all the operations in time O(s\delta^{-1} + \eps^{-1}). The improvement is twofold: our redundancy can be lowered parametrically and, fixing $s = O(1)$, we get a constant-time FID whose space is B(n,m) + O(m^\eps/\poly{n}) bits, for sufficiently large $m$. This is a significant improvement compared to the previous bounds for the general case

Eimeria species occurrence varies between geographic regions and poultry production systems and may influence parasite genetic diversity

Coccidiosis is one of the biggest challenges faced by the global poultry industry. Recent studies have highlighted the ubiquitous distribution of all Eimeria species which can cause this disease in chickens, but intriguingly revealed a regional divide in genetic diversity and population structure for at least one species, Eimeria tenella. The drivers associated with such distinct geographic variation are unclear, but may impact on the occurrence and extent of resistance to anticoccidial drugs and future subunit vaccines. India is one of the largest poultry producers in the world and includes a transition between E. tenella populations defined by high and low genetic diversity. The aim of this study was to identify risk factors associated with the prevalence of Eimeria species defined by high and low pathogenicity in northern and southern states of India, and seek to understand factors which vary between the regions as possible drivers for differential genetic variation. Faecal samples and data relating to farm characteristics and management were collected from 107 farms from northern India and 133 farms from southern India. Faecal samples were analysed using microscopy and PCR to identify Eimeria occurrence. Multiple correspondence analysis was applied to transform correlated putative risk factors into a smaller number of synthetic uncorrelated factors. Hierarchical cluster analysis was used to identify poultry farm typologies, revealing three distinct clusters in the studied regions. The association between clusters and presence of Eimeria species was assessed by logistic regression. The study found that large-scale broiler farms in the north were at greatest risk of harbouring any Eimeria species and a larger proportion of such farms were positive for E. necatrix, the most pathogenic species. Comparison revealed a more even distribution for E. tenella across production systems in south India, but with a lower overall occurrence. Such a polarised region- and system-specific distribution may contribute to the different levels of genetic diversity observed previously in India and may influence parasite population structure across much of Asia and Africa. The findings of the study can be used to prioritise target farms to launch and optimise appropriate anticoccidial strategies for long-term control

Cryptic Eimeria genotypes are common across the southern but not northern hemisphere

The phylum Apicomplexa includes parasites of medical, zoonotic and veterinary significance. Understanding the global distribution and genetic diversity of these protozoa is of fundamental importance for efficient, robust and long-lasting methods of control. Eimeria spp. cause intestinal coccidiosis in all major livestock animals and are the most important parasites of domestic chickens in terms of both economic impact and animal welfare. Despite having significant negative impacts on the efficiency of food production, many fundamental questions relating to the global distribution and genetic variation of Eimeria spp. remain largely unanswered. Here, we provide the broadest map yet of Eimeria occurrence for domestic chickens, confirming that all the known species (Eimeria acervulina, Eimeria brunetti, Eimeria maxima, Eimeria mitis, Eimeria necatrix, Eimeria praecox, Eimeria tenella) are present in all six continents where chickens are found (including 21 countries). Analysis of 248 internal transcribed spacer sequences derived from 17 countries provided evidence of possible allopatric diversity for species such as E. tenella (FST values ⩽0.34) but not E. acervulina and E. mitis, and highlighted a trend towards widespread genetic variance. We found that three genetic variants described previously only in Australia and southern Africa (operational taxonomic units x, y and z) have a wide distribution across the southern, but not the northern hemisphere. While the drivers for such a polarised distribution of these operational taxonomic unit genotypes remains unclear, the occurrence of genetically variant Eimeria may pose a risk to food security and animal welfare in Europe and North America should these parasites spread to the northern hemisphere

Population, genetic, and antigenic diversity of the apicomplexan Eimeria tenella and their relevance to vaccine development

The phylum Apicomplexa includes serious pathogens of humans and animals. Understanding the distribution and population structure of these protozoan parasites is of fundamental importance to explain disease epidemiology and develop sustainable controls. Predicting the likely efficacy and longevity of subunit vaccines in field populations relies on knowledge of relevant preexisting antigenic diversity, population structure, the likelihood of coinfection by genetically distinct strains, and the efficiency of cross-fertilization. All four of these factors have been investigated for Plasmodium species parasites, revealing both clonal and panmictic population structures with exceptional polymorphism associated with immunoprotective antigens such as apical membrane antigen 1 (AMA1). For the coccidian Toxoplasma gondii only genomic diversity and population structure have been defined in depth so far; for the closely related Eimeria species, all four variables are currently unknown. Using Eimeria tenella, a major cause of the enteric disease coccidiosis, which exerts a profound effect on chicken productivity and welfare, we determined population structure, genotype distribution, and likelihood of cross-fertilization during coinfection and also investigated the extent of naturally occurring antigenic diversity for the E. tenella AMA1 homolog. Using genome-wide Sequenom SNP-based haplotyping, targeted sequencing, and single-cell genotyping, we show that in this coccidian the functionality of EtAMA1 appears to outweigh immune evasion. This result is in direct contrast to the situation in Plasmodium and most likely is underpinned by the biology of the direct and acute coccidian life cycle in the definitive host

Hyperoxemia and excess oxygen use in early acute respiratory distress syndrome : Insights from the LUNG SAFE study

Publisher Copyright: © 2020 The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.Background: Concerns exist regarding the prevalence and impact of unnecessary oxygen use in patients with acute respiratory distress syndrome (ARDS). We examined this issue in patients with ARDS enrolled in the Large observational study to UNderstand the Global impact of Severe Acute respiratory FailurE (LUNG SAFE) study. Methods: In this secondary analysis of the LUNG SAFE study, we wished to determine the prevalence and the outcomes associated with hyperoxemia on day 1, sustained hyperoxemia, and excessive oxygen use in patients with early ARDS. Patients who fulfilled criteria of ARDS on day 1 and day 2 of acute hypoxemic respiratory failure were categorized based on the presence of hyperoxemia (PaO2 > 100 mmHg) on day 1, sustained (i.e., present on day 1 and day 2) hyperoxemia, or excessive oxygen use (FIO2 ≥ 0.60 during hyperoxemia). Results: Of 2005 patients that met the inclusion criteria, 131 (6.5%) were hypoxemic (PaO2 < 55 mmHg), 607 (30%) had hyperoxemia on day 1, and 250 (12%) had sustained hyperoxemia. Excess FIO2 use occurred in 400 (66%) out of 607 patients with hyperoxemia. Excess FIO2 use decreased from day 1 to day 2 of ARDS, with most hyperoxemic patients on day 2 receiving relatively low FIO2. Multivariate analyses found no independent relationship between day 1 hyperoxemia, sustained hyperoxemia, or excess FIO2 use and adverse clinical outcomes. Mortality was 42% in patients with excess FIO2 use, compared to 39% in a propensity-matched sample of normoxemic (PaO2 55-100 mmHg) patients (P = 0.47). Conclusions: Hyperoxemia and excess oxygen use are both prevalent in early ARDS but are most often non-sustained. No relationship was found between hyperoxemia or excessive oxygen use and patient outcome in this cohort. Trial registration: LUNG-SAFE is registered with ClinicalTrials.gov, NCT02010073publishersversionPeer reviewe

Global burden of 369 diseases and injuries in 204 countries and territories, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019

Background: In an era of shifting global agendas and expanded emphasis on non-communicable diseases and injuries along with communicable diseases, sound evidence on trends by cause at the national level is essential. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) provides a systematic scientific assessment of published, publicly available, and contributed data on incidence, prevalence, and mortality for a mutually exclusive and collectively exhaustive list of diseases and injuries. Methods: GBD estimates incidence, prevalence, mortality, years of life lost (YLLs), years lived with disability (YLDs), and disability-adjusted life-years (DALYs) due to 369 diseases and injuries, for two sexes, and for 204 countries and territories. Input data were extracted from censuses, household surveys, civil registration and vital statistics, disease registries, health service use, air pollution monitors, satellite imaging, disease notifications, and other sources. Cause-specific death rates and cause fractions were calculated using the Cause of Death Ensemble model and spatiotemporal Gaussian process regression. Cause-specific deaths were adjusted to match the total all-cause deaths calculated as part of the GBD population, fertility, and mortality estimates. Deaths were multiplied by standard life expectancy at each age to calculate YLLs. A Bayesian meta-regression modelling tool, DisMod-MR 2.1, was used to ensure consistency between incidence, prevalence, remission, excess mortality, and cause-specific mortality for most causes. Prevalence estimates were multiplied by disability weights for mutually exclusive sequelae of diseases and injuries to calculate YLDs. We considered results in the context of the Socio-demographic Index (SDI), a composite indicator of income per capita, years of schooling, and fertility rate in females younger than 25 years. Uncertainty intervals (UIs) were generated for every metric using the 25th and 975th ordered 1000 draw values of the posterior distribution. Findings: Global health has steadily improved over the past 30 years as measured by age-standardised DALY rates. After taking into account population growth and ageing, the absolute number of DALYs has remained stable. Since 2010, the pace of decline in global age-standardised DALY rates has accelerated in age groups younger than 50 years compared with the 1990–2010 time period, with the greatest annualised rate of decline occurring in the 0–9-year age group. Six infectious diseases were among the top ten causes of DALYs in children younger than 10 years in 2019: lower respiratory infections (ranked second), diarrhoeal diseases (third), malaria (fifth), meningitis (sixth), whooping cough (ninth), and sexually transmitted infections (which, in this age group, is fully accounted for by congenital syphilis; ranked tenth). In adolescents aged 10–24 years, three injury causes were among the top causes of DALYs: road injuries (ranked first), self-harm (third), and interpersonal violence (fifth). Five of the causes that were in the top ten for ages 10–24 years were also in the top ten in the 25–49-year age group: road injuries (ranked first), HIV/AIDS (second), low back pain (fourth), headache disorders (fifth), and depressive disorders (sixth). In 2019, ischaemic heart disease and stroke were the top-ranked causes of DALYs in both the 50–74-year and 75-years-and-older age groups. Since 1990, there has been a marked shift towards a greater proportion of burden due to YLDs from non-communicable diseases and injuries. In 2019, there were 11 countries where non-communicable disease and injury YLDs constituted more than half of all disease burden. Decreases in age-standardised DALY rates have accelerated over the past decade in countries at the lower end of the SDI range, while improvements have started to stagnate or even reverse in countries with higher SDI. Interpretation: As disability becomes an increasingly large component of disease burden and a larger component of health expenditure, greater research and developm nt investment is needed to identify new, more effective intervention strategies. With a rapidly ageing global population, the demands on health services to deal with disabling outcomes, which increase with age, will require policy makers to anticipate these changes. The mix of universal and more geographically specific influences on health reinforces the need for regular reporting on population health in detail and by underlying cause to help decision makers to identify success stories of disease control to emulate, as well as opportunities to improve. Funding: Bill & Melinda Gates Foundation. © 2020 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 licens