Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

A Rydberg Quantum Simulator

Following Feynman and as elaborated on by Lloyd, a universal quantum simulator (QS) is a controlled quantum device which reproduces the dynamics of any other many particle quantum system with short range interactions. This dynamics can refer to both coherent Hamiltonian and dissipative open system evolution. We investigate how laser excited Rydberg atoms in large spacing optical or magnetic lattices can provide an efficient implementation of a universal QS for spin models involving (high order) n-body interactions. This includes the simulation of Hamiltonians of exotic spin models involving n-particle constraints such as the Kitaev toric code, color code, and lattice gauge theories with spin liquid phases. In addition, it provides the ingredients for dissipative preparation of entangled states based on engineering n-particle reservoir couplings. The key basic building blocks of our architecture are efficient and high-fidelity n-qubit entangling gates via auxiliary Rydberg atoms, including a possible dissipative time step via optical pumping. This allows to mimic the time evolution of the system by a sequence of fast, parallel and high-fidelity n-particle coherent and dissipative Rydberg gates.Comment: 8 pages, 4 figure

Determining the neurotransmitter concentration profile at active synapses

Establishing the temporal and concentration profiles of neurotransmitters during synaptic release is an essential step towards understanding the basic properties of inter-neuronal communication in the central nervous system. A variety of ingenious attempts has been made to gain insights into this process, but the general inaccessibility of central synapses, intrinsic limitations of the techniques used, and natural variety of different synaptic environments have hindered a comprehensive description of this fundamental phenomenon. Here, we describe a number of experimental and theoretical findings that has been instrumental for advancing our knowledge of various features of neurotransmitter release, as well as newly developed tools that could overcome some limits of traditional pharmacological approaches and bring new impetus to the description of the complex mechanisms of synaptic transmission

Mapping and modelling the geographical distribution and environmental limits of podoconiosis in Ethiopia

BACKGROUND Ethiopia is assumed to have the highest burden of podoconiosis globally, but the geographical distribution and environmental limits and correlates are yet to be fully investigated. In this paper we use data from a nationwide survey to address these issues. METHODOLOGY Our analyses are based on data arising from the integrated mapping of podoconiosis and lymphatic filariasis (LF) conducted in 2013, supplemented by data from an earlier mapping of LF in western Ethiopia in 2008-2010. The integrated mapping used woreda (district) health offices' reports of podoconiosis and LF to guide selection of survey sites. A suite of environmental and climatic data and boosted regression tree (BRT) modelling was used to investigate environmental limits and predict the probability of podoconiosis occurrence. PRINCIPAL FINDINGS Data were available for 141,238 individuals from 1,442 communities in 775 districts from all nine regional states and two city administrations of Ethiopia. In 41.9% of surveyed districts no cases of podoconiosis were identified, with all districts in Affar, Dire Dawa, Somali and Gambella regional states lacking the disease. The disease was most common, with lymphoedema positivity rate exceeding 5%, in the central highlands of Ethiopia, in Amhara, Oromia and Southern Nations, Nationalities and Peoples regional states. BRT modelling indicated that the probability of podoconiosis occurrence increased with increasing altitude, precipitation and silt fraction of soil and decreased with population density and clay content. Based on the BRT model, we estimate that in 2010, 34.9 (95% confidence interval [CI]: 20.2-51.7) million people (i.e. 43.8%; 95% CI: 25.3-64.8% of Ethiopia's national population) lived in areas environmentally suitable for the occurrence of podoconiosis. CONCLUSIONS Podoconiosis is more widespread in Ethiopia than previously estimated, but occurs in distinct geographical regions that are tied to identifiable environmental factors. The resultant maps can be used to guide programme planning and implementation and estimate disease burden in Ethiopia. This work provides a framework with which the geographical limits of podoconiosis could be delineated at a continental scale

Ecological conditions determine extinction risk in co-evolving bacteria-phage populations.

BACKGROUND: Antagonistic coevolution between bacteria and their viral parasites, phage, drives continual evolution of resistance and infectivity traits through recurrent cycles of adaptation and counter-adaptation. Both partners are vulnerable to extinction through failure of adaptation. Environmental conditions may impose unequal abiotic selection pressures on each partner, destabilising the coevolutionary relationship and increasing the extinction risk of one partner. In this study we explore how the degree of population mixing and resource supply affect coevolution-induced extinction risk by coevolving replicate populations of Pseudomonas fluorescens SBW25 with its associated lytic phage SBW25Ф2 under four treatment regimens incorporating low and high resource availability with mixed or static growth conditions. RESULTS: We observed an increased risk of phage extinction under population mixing, and in low resource conditions. High levels of evolved bacterial resistance promoted phage extinction at low resources under both mixed and static conditions, whereas phage populations could survive when phage susceptible bacterial genotypes rose to high frequency. CONCLUSIONS: These findings demonstrate that phage extinction risk is influenced by multiple abiotic conditions, which together act to destabilise the bacteria-phage coevolutionary relationship. The risk of coevolution-induced extinction is therefore dependent on the ecological context

Analytic philosophy for biomedical research: the imperative of applying yesterday's timeless messages to today's impasses

The mantra that "the best way to predict the future is to invent it" (attributed to the computer scientist Alan Kay) exemplifies some of the expectations from the technical and innovative sides of biomedical research at present. However, for technical advancements to make real impacts both on patient health and genuine scientific understanding, quite a number of lingering challenges facing the entire spectrum from protein biology all the way to randomized controlled trials should start to be overcome. The proposal in this chapter is that philosophy is essential in this process. By reviewing select examples from the history of science and philosophy, disciplines which were indistinguishable until the mid-nineteenth century, I argue that progress toward the many impasses in biomedicine can be achieved by emphasizing theoretical work (in the true sense of the word 'theory') as a vital foundation for experimental biology. Furthermore, a philosophical biology program that could provide a framework for theoretical investigations is outlined

Hybridization and hybrid speciation under global change

An unintended consequence of global change is an increase in opportunities for hybridization among previously isolated lineages. Here we illustrate how global change can facilitate the breakdown of reproductive barriers and the formation of hybrids, drawing on the flora of the British Isles for insight. Although global change may ameliorate some of the barriers preventing hybrid establishment, for example by providing new ecological niches for hybrids, it will have limited effects on environment-independent post-zygotic barriers. For example, genic incompatibilities and differences in chromosome numbers and structure within hybrid genomes are unlikely to be affected by global change. We thus speculate that global change will have a larger effect on eroding pre-zygotic barriers (eco-geographical isolation and phenology) than post-zygotic barriers, shifting the relative importance of these two classes of reproductive barriers from what is usually seen in naturally produced hybrids where pre-zygotic barriers are the largest contributors to reproductive isolation. Although the long-term fate of neo-hybrids is still to be determined, the massive impact of global change on the dynamics and distribution of biodiversity generates an unprecedented opportunity to study large numbers of unpredicted, and often replicated, hybridization ‘experiments’, allowing us to peer into the birth and death of evolutionary lineages

Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in Relativity

Theory of disk accretion onto supermassive black holes

Accretion onto supermassive black holes produces both the dramatic phenomena associated with active galactic nuclei and the underwhelming displays seen in the Galactic Center and most other nearby galaxies. I review selected aspects of the current theoretical understanding of black hole accretion, emphasizing the role of magnetohydrodynamic turbulence and gravitational instabilities in driving the actual accretion and the importance of the efficacy of cooling in determining the structure and observational appearance of the accretion flow. Ongoing investigations into the dynamics of the plunging region, the origin of variability in the accretion process, and the evolution of warped, twisted, or eccentric disks are summarized.Comment: Mostly introductory review, to appear in "Supermassive black holes in the distant Universe", ed. A.J. Barger, Kluwer Academic Publishers, in pres

Multiview classification and dimensionality reduction of scalp and intracranial EEG data through tensor factorisation

Electroencephalography (EEG) signals arise as a mixture of various neural processes that occur in different spatial, frequency and temporal locations. In classification paradigms, algorithms are developed that can distinguish between these processes. In this work, we apply tensor factorisation to a set of EEG data from a group of epileptic patients and factorise the data into three modes; space, time and frequency with each mode containing a number of components or signatures. We train separate classifiers on various feature sets corresponding to complementary combinations of those modes and components and test the classification accuracy of each set. The relative influence on the classification accuracy of the respective spatial, temporal or frequency signatures can then be analysed and useful interpretations can be made. Additionaly, we show that through tensor factorisation we can perform dimensionality reduction by evaluating the classification performance with regards to the number mode components and by rejecting components with insignificant contribution to the classification accuracy