Global Versus Local Computations: Fast Computing with Identifiers

This paper studies what can be computed by using probabilistic local interactions with agents with a very restricted power in polylogarithmic parallel time. It is known that if agents are only finite state (corresponding to the Population Protocol model by Angluin et al.), then only semilinear predicates over the global input can be computed. In fact, if the population starts with a unique leader, these predicates can even be computed in a polylogarithmic parallel time. If identifiers are added (corresponding to the Community Protocol model by Guerraoui and Ruppert), then more global predicates over the input multiset can be computed. Local predicates over the input sorted according to the identifiers can also be computed, as long as the identifiers are ordered. The time of some of those predicates might require exponential parallel time. In this paper, we consider what can be computed with Community Protocol in a polylogarithmic number of parallel interactions. We introduce the class CPPL corresponding to protocols that use $O(n\log^k n)$, for some k, expected interactions to compute their predicates, or equivalently a polylogarithmic number of parallel expected interactions. We provide some computable protocols, some boundaries of the class, using the fact that the population can compute its size. We also prove two impossibility results providing some arguments showing that local computations are no longer easy: the population does not have the time to compare a linear number of consecutive identifiers. The Linearly Local languages, such that the rational language $(ab)^*$, are not computable.Comment: Long version of SSS 2016 publication, appendixed version of SIROCCO 201

Numerical Integration of the Master Equation in Some Models of Stochastic Epidemiology

The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation – up to a desired precision – in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

Estimating the Duration of Pertussis Immunity Using Epidemiological Signatures

Case notifications of pertussis have shown an increase in a number of countries with high rates of routine pediatric immunization. This has led to significant public health concerns over a possible pertussis re-emergence. A leading proposed explanation for the observed increase in incidence is the loss of immunity to pertussis, which is known to occur after both natural infection and vaccination. Little is known, however, about the typical duration of immunity and its epidemiological implications. Here, we analyze a simple mathematical model, exploring specifically the inter-epidemic period and fade-out frequency. These predictions are then contrasted with detailed incidence data for England and Wales. We find model output to be most sensitive to assumptions concerning naturally acquired immunity, which allows us to estimate the average duration of immunity. Our results support a period of natural immunity that is, on average, long-lasting (at least 30 years) but inherently variable

The association between timed up and go test and history of falls: The Tromsø study

BACKGROUND: Fall-related injuries in older adults are a major health problem. Although the aetiology of falls is multifactorial, physical factors are assumed to contribute significantly. The "Timed up and go test" (TUG) is designed to measure basic mobility function. This report evaluates the association between TUG times and history of falls. METHODS: A retrospective, observational, population-based study was conducted on 414 men and 560 women with mean age 77.5 (SD 2.3). TUG time and falls during the previous 12 months were recorded. Covariates were age, sex, medical history and health-related mobility problems. Means, confidence intervals and test characteristics for TUG were calculated. Odds ratios and influence of covariates were examined by logistic regression. RESULTS: The mean TUG time was 11.1s (SD 2.5) among male non-fallers and 13.0s (SD 7.8) among fallers. The difference was 1.9s (95%CI 0.9–3.0). The odds ratio for fallers being in the upper quartile was 2.1 (95%CI 1.4–3.3). Adjusted for covariates, the odds ratio was (OR = 1.8, 95%CI 1.1–2.9). The corresponding mean was 13.0s (SD 5.74) among female non-fallers and 13.9s (SD 8.5) among fallers. The difference was 0.9 (95%CI -0.3–2.1). The odds ratio for fallers being in upper quartile was 1.0 (95%CI 0.7–1.4). The area under the ROC curve was 0.50 (95%CI 0.45–0.55) in women and 0.56 (95%CI 0.50–0.62) in men. CONCLUSION: TUG is statistically associated with a history of falls in men but not in women. The ability to classify fallers is poor, and the clinical value of the association is therefore limited

A Search for Energy Minimized Sequences of Proteins

In this paper, we present numerical evidence that supports the notion of minimization in the sequence space of proteins for a target conformation. We use the conformations of the real proteins in the Protein Data Bank (PDB) and present computationally efficient methods to identify the sequences with minimum energy. We use edge-weighted connectivity graph for ranking the residue sites with reduced amino acid alphabet and then use continuous optimization to obtain the energy-minimizing sequences. Our methods enable the computation of a lower bound as well as a tight upper bound for the energy of a given conformation. We validate our results by using three different inter-residue energy matrices for five proteins from protein data bank (PDB), and by comparing our energy-minimizing sequences with 80 million diverse sequences that are generated based on different considerations in each case. When we submitted some of our chosen energy-minimizing sequences to Basic Local Alignment Search Tool (BLAST), we obtained some sequences from non-redundant protein sequence database that are similar to ours with an E-value of the order of 10-7. In summary, we conclude that proteins show a trend towards minimizing energy in the sequence space but do not seem to adopt the global energy-minimizing sequence. The reason for this could be either that the existing energy matrices are not able to accurately represent the inter-residue interactions in the context of the protein environment or that Nature does not push the optimization in the sequence space, once it is able to perform the function

Quasi-Neutral theory of epidemic outbreaks

Some epidemics have been empirically observed to exhibit outbreaks of all possible sizes, i.e., to be scalefree or scale-invariant. Different explanations for this finding have been put forward; among them there is a model for "accidental pathogens" which leads to power-law distributed outbreaks without apparent need of parameter fine tuning. This model has been claimed to be related to self-organized criticality, and its critical properties have been conjectured to be related to directed percolation. Instead, we show that this is a (quasi) neutral model, analogous to those used in Population Genetics and Ecology, with the same critical behavior as the voter-model, i.e. the theory of accidental pathogens is a (quasi)-neutral theory. This analogy allows us to explain all the system phenomenology, including generic scale invariance and the associated scaling exponents, in a parsimonious and simple way.Comment: 13 pages, 6 figures Accepted for publication in PLoS ONE the text have been modified in orden to improve the figure's resolutio

The Personal and Health Service Impact of Falls in 85 Year Olds: Cross-Sectional Findings from the Newcastle 85+ Cohort Study

Falls are common in older people and increase in prevalence with advancing old age. There is limited knowledge about their impact in those aged 85 years and older, the fastest growing age group of the population. We investigated the prevalence and impact of falls, and the overlap between falls, dizziness and blackouts, in a population-based sample of 85 year olds.Cross-sectional analysis of baseline data from Newcastle 85+ Cohort Study.Primary care, North-East England.816 men and women aged 85 years.Structured interview with research nurse. Cost-consequence analysis of fall-related healthcare costs.Over 38% (313/816) of participants had fallen at least once in the previous 12 months and of these: 10.6% (33/312) sustained a fracture, 30.1% (94/312) attended an emergency department, and 12.8% (40/312) were admitted to hospital. Only 37.2% (115/309) of fallers had specifically discussed their falls problem with their general practitioner and only 12.7% (39/308) had seen a falls specialist. The average annual healthcare cost per faller was estimated at £202 (inter-quartile range £174-£231) or US$329 ($284-$377). 'Worry about falling' was experienced by 42.0% (128/305) of fallers, 'loss of confidence' by 40.0% (122/305), and 'going out less often' by 25.9% (79/305); each was significantly more common in women, odds ratios (95% confidence interval) for women: men of 2.63 (1.45-4.55), 4.00 (2.27-7.14), and 2.86 (1.54-5.56) respectively. Dizziness and blackouts were reported by 40.0% (318/796) and 6.4% (52/808) of participants respectively. There was marked overlap in the report of falls, dizziness and blackouts.Falls in 85 year olds are very common, associated with considerable psychological and physical morbidity, and have high impact on healthcare services. Wider use of fall prevention services is needed. Significant expansion in acute and preventative services is required in view of the rapid growth in this age group

Theory and practice of social norms interventions: eight common pitfalls.

BACKGROUND: Recently, Global Health practitioners, scholars, and donors have expressed increased interest in "changing social norms" as a strategy to promote health and well-being in low and mid-income countries (LMIC). Despite this burgeoning interest, the ability of practitioners to use social norm theory to inform health interventions varies widely. MAIN BODY: Here, we identify eight pitfalls that practitioners must avoid as they plan to integrate a social norms perspective in their interventions, as well as eight learnings. These learnings are: 1) Social norms and attitudes are different; 2) Social norms and attitudes can coincide; 3) Protective norms can offer important resources for achieving effective social improvement in people's health-related practices; 4) Harmful practices are sustained by a matrix of factors that need to be understood in their interactions; 5) The prevalence of a norm is not necessarily a sign of its strength; 6) Social norms can exert both direct and indirect influence; 7) Publicising the prevalence of a harmful practice can make things worse; 8) People-led social norm change is both the right and the smart thing to do. CONCLUSIONS: As the understanding of how norms evolve in LMIC advances, practitioners will develop greater understanding of what works to help people lead change in harmful norms within their contexts. Awareness of these pitfalls has helped several of them increase the effectiveness of their interventions addressing social norms in the field. We are confident that others will benefit from these reflections as well