Equation-free modeling of evolving diseases: Coarse-grained computations with individual-based models

We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. % Sidestepping the necessity of obtaining explicit population-level models, the approach analyzes the (unavailable in closed form) `coarse' macroscopic equations, estimating the necessary quantities through appropriately initialized, short `bursts' of individual-based dynamic simulation. % We illustrate this approach by analyzing a stochastic and discrete model for the evolution of disease agents caused by point mutations within individual hosts. % Building up from classical SIR and SIRS models, our example uses a one-dimensional lattice for variant space, and assumes a finite number of individuals. % Macroscopic computational tasks enabled through this approach include stationary state computation, coarse projective integration, parametric continuation and stability analysis.Comment: 16 pages, 8 figure

From single steps to mass migration: the problem of scale in the movement ecology of the Serengeti wildebeest

A central question in ecology is how to link processes that occur over different scales. The daily interactions of individual organisms ultimately determine community dynamics, population fluctuations and the functioning of entire ecosystems. Observations of these multiscale ecological processes are constrained by various technological, biological or logistical issues, and there are often vast discrepancies between the scale at which observation is possible and the scale of the question of interest. Animal movement is characterized by processes that act over multiple spatial and temporal scales. Second-by-second decisions accumulate to produce annual movement patterns. Individuals influence, and are influenced by, collective movement decisions, which then govern the spatial distribution of populations and the connectivity of meta-populations. While the field of movement ecology is experiencing unprecedented growth in the availability of movement data, there remain challenges in integrating observations with questions of ecological interest. In this article, we present the major challenges of addressing these issues within the context of the Serengeti wildebeest migration, a keystone ecological phenomena that crosses multiple scales of space, time and biological complexity. This article is part of the theme issue ’Collective movement ecology’

Trajectories of health-related quality of life in children with epilepsy: A cohort study

Purpose Little is known about subgroups of children with epilepsy who may experience less favorable outcomes over time. The objectives of this study were to document trajectories of health-related quality of life (HRQL) and to identify predictors of the trajectory group in children with new-onset epilepsy. Methods Data were obtained from the Health Related Quality of Life in Children with Epilepsy Study, a prospective multisite study of children 4-12 years old with new-onset epilepsy followed for 24 months. Health-related quality of life was measured using the Quality of Life in Childhood Epilepsy questionnaire. Trajectories of HRQL were investigated using latent class trajectory modeling. Multinomial logistic regression was used to identify child, parent, and family predictors of HRQL trajectories. Key Findings A total of 374 families responded at baseline and 283 (76%) completed the study. Five HRQL trajectories were observed: low-increasing (4%), moderate-decreasing (12%), moderate-increasing (22%), high-increasing (32%), and high-stable (30%). Many children in the low-increasing, moderate-increasing, high-increasing, and high-stable had clinically meaningful improvements in HRQL: 82%, 47%, 63%, and 44%, respectively. In contrast, the majority of children in the moderate-decreasing group (56%) experienced clinically meaningful declines in their HRQL. Factors predicting trajectories were number of antiepileptic drugs prescribed, presence of comorbid behavior or cognitive problems, parent depression, and family functioning and demands. Significance Results suggested that children with epilepsy are not homogenous but rather consist of groups with different trajectories and unique predictors of HRQL. Problems associated with child behavior and cognition were the strongest predictors identified. Given that several risk factors are modifiable, it is important to examine these as potential targets within a family-centered framework to improve HRQL of children with new-onset epilepsy. © Wiley Periodicals, Inc. © 2013 International League Against Epilepsy

Quality of life in children with new-onset epilepsy; A 2-year prospective cohort study

Objectives: To assess health-related quality of life (HRQL) over 2 years in children 4-12 years old with new-onset epilepsy and risk factors. Methods: Data are from a multicenter prospective cohort study, the Health-Related Quality of Life Study in Children with Epilepsy Study (HERQULES). Parents reported on children\u27s HRQL and family factors and neurologists on clinical characteristics 4 times. Mean subscale and summary scores were computed for HRQL. Individual growth curve models identified trajectories of change in HRQL scores. Multiple regression identified baseline risk factors for HRQL 2 years later. Results: A total of 374 (82%) questionnaires were returned postdiagnosis and 283 (62%) of eligible parents completed all 4. Growth rates for HRQL summary scores were most rapid during the first 6 months and then stabilized. About one-half experienced clinically meaningful improvements in HRQL, one-third maintained their same level, and one-fifth declined. Compared with the general population, at 2 years our sample scored significantly lower on one-third of CHQ subscales and the psychosocial summary. After controlling for baseline HRQL, cognitive problems, poor family functioning, and high family demands were risk factors for poor HRQL 2 years later. Conclusions: On average, HRQL was relatively good but with highly variable individual trajectories. At least one-half did not experience clinically meaningful improvements or declined over 2 years. Cognitive problems were the strongest risk factor for compromised HRQL 2 years after diagnosis and may be largely responsible for declines in the HRQL of children newly diagnosed with epilepsy. © 2012 by AAN Enterprises, Inc

Dynamical Mass Generation of Composite Dirac Fermions and Fractional Quantum Hall Effects near Charge Neutrality in Graphene

We develop a composite Dirac fermion theory for the fractional quantum Hall effects (QHE) near charge neutrality in graphene. We show that the interactions between the composite Dirac fermions lead to dynamical mass generation through exciton condensation. The four-fold spin-valley degeneracy is fully lifted due to the mass generation and the exchange effects such that the odd-denominator fractional QHE observed in the vicinity of charge neutrality can be understood in terms of the integer QHE of the composite Dirac fermions. At the filling factor $\nu=1/2$, we show that the massive composite Dirac fermion liquid is unstable against chiral p-wave pairing for weak Coulomb interactions and the ground state is a paired nonabelian state described by the Moore-Read Pfaffian in the long wavelength limit.Comment: Extended, published version, 9 pages, 3 figure

How Can Vaccines Against Influenza and Other Viral Diseases Be Made More Effective?

A large fraction of the world’s most widespread and problematic pathogens, such as the influenza virus, seem to persist in nature by evading host immune responses by inducing immunity to genetically and phenotypically plastic epitopes (aka antigenic variation). The more recent re-emergence of pandemic influenza A/ H1N1 and avian H5N1 viruses has called attention to the urgent need for more effective influenza vaccines. Developing such vaccines will require more than just moving from an egg-based to a tissueculture–based manufacturing process. It will also require a new conceptual understanding of pathogen–host interactions, as well as new approaches and technologies to circumvent immune evasion by pathogens capable of more genetic variation. Here, we discuss these challenges, focusing on some potentially fruitful directions for future research

Patchiness and Demographic Noise in Three Ecological Examples

Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only -at most- local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy

Non-Abelian Anyons and Topological Quantum Computation

Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as {\it Non-Abelian anyons}, meaning that they obey {\it non-Abelian braiding statistics}. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations which are necessary for quantum computation are carried out by braiding quasiparticles, and then measuring the multi-quasiparticle states. The fault-tolerance of a topological quantum computer arises from the non-local encoding of the states of the quasiparticles, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the \nu=5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultra-cold atoms in optical lattices and thin film superconductors. In this review article, we describe current research in this field, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. We address both the mathematical underpinnings of topological quantum computation and the physics of the subject using the \nu=5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.Comment: Final Accepted form for RM

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

Attention on Weak Ties in Social and Communication Networks

Granovetter's weak tie theory of social networks is built around two central hypotheses. The first states that strong social ties carry the large majority of interaction events; the second maintains that weak social ties, although less active, are often relevant for the exchange of especially important information (e.g., about potential new jobs in Granovetter's work). While several empirical studies have provided support for the first hypothesis, the second has been the object of far less scrutiny. A possible reason is that it involves notions relative to the nature and importance of the information that are hard to quantify and measure, especially in large scale studies. Here, we search for empirical validation of both Granovetter's hypotheses. We find clear empirical support for the first. We also provide empirical evidence and a quantitative interpretation for the second. We show that attention, measured as the fraction of interactions devoted to a particular social connection, is high on weak ties --- possibly reflecting the postulated informational purposes of such ties --- but also on very strong ties. Data from online social media and mobile communication reveal network-dependent mixtures of these two effects on the basis of a platform's typical usage. Our results establish a clear relationships between attention, importance, and strength of social links, and could lead to improved algorithms to prioritize social media content