Model hierarchies in edge-based compartmental modeling for infectious disease spread.
ABSTRACT: We consider the family of edge-based compartmental models for epidemic spread developed in Miller et al. (J R Soc Interface 9(70):890-906, 2012). These models allow for a range of complex behaviors, and in particular allow us to explicitly incorporate duration of a contact into our mathematical models. Our focus here is to identify conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide conditions under which it is appropriate to use the standard mass action SIR model, and we show what happens when these conditions fail. Using our hierarchy, we provide a procedure leading to the choice of the appropriate model for a given population. Our result about the convergence of models to the mass action model gives clear, rigorous conditions under which the mass action model is accurate.
Project description:Exposure to stress can affect the establishment of dominance hierarchies. In our model, a social hierarchy established by two male rats during a first encounter is not maintained 1 week later. If one of the two rats is stressed, the stressed rat becomes subordinate and the hierarchy that is formed is maintained. In this study, we investigated the changes in the expression of oxytocin (Otr) and vasopressin (V1aR) receptor genes in the medial amygdala (MeA) and the lateral septum (LS) in the hours following hierarchy establishment under both stressed and basal conditions. We found that the potentiation of a social hierarchy induced by stress is accompanied by social status- and region-specific changes in the expression of Otr mRNA in the MeA 3?h after the social encounter. At this time point, no evidence was found for the regulation of V1aR mRNA in any of the brain regions examined. Results from pharmacological experiments involving the microinfusion of a specific OTR antagonist immediately after the acquisition of a subordinate status under basal, non-stress conditions suggested a role for this receptor in the MeA on the long-term establishment of the subordinate status. Altogether, these findings highlight a role for the oxytocinergic system in the mechanisms through which stress facilitates the long-term establishment of a social hierarchy.
Project description:Tagging items with descriptive annotations or keywords is a very natural way to compress and highlight information about the properties of the given entity. Over the years several methods have been proposed for extracting a hierarchy between the tags for systems with a "flat", egalitarian organization of the tags, which is very common when the tags correspond to free words given by numerous independent people. Here we present a complete framework for automated tag hierarchy extraction based on tag occurrence statistics. Along with proposing new algorithms, we are also introducing different quality measures enabling the detailed comparison of competing approaches from different aspects. Furthermore, we set up a synthetic, computer generated benchmark providing a versatile tool for testing, with a couple of tunable parameters capable of generating a wide range of test beds. Beside the computer generated input we also use real data in our studies, including a biological example with a pre-defined hierarchy between the tags. The encouraging similarity between the pre-defined and reconstructed hierarchy, as well as the seemingly meaningful hierarchies obtained for other real systems indicate that tag hierarchy extraction is a very promising direction for further research with a great potential for practical applications. Tags have become very prevalent nowadays in various online platforms ranging from blogs through scientific publications to protein databases. Furthermore, tagging systems dedicated for voluntary tagging of photos, films, books, etc. with free words are also becoming popular. The emerging large collections of tags associated with different objects are often referred to as folksonomies, highlighting their collaborative origin and the "flat" organization of the tags opposed to traditional hierarchical categorization. Adding a tag hierarchy corresponding to a given folksonomy can very effectively help narrowing or broadening the scope of search. Moreover, recommendation systems could also benefit from a tag hierarchy.
Project description:Economic evaluations of infectious disease control interventions frequently use dynamic compartmental epidemic models. Such models capture heterogeneity in risk of infection by stratifying the population into discrete risk groups, thus approximating what is typically continuous variation in risk. An important open question is whether and how different risk stratification choices influence model predictions of intervention effects. We develop equivalent Susceptible-Infected-Susceptible (SIS) dynamic transmission models: an unstratified model, a model stratified into a high-risk and low-risk group, and a model with an arbitrary number of risk groups. Absent intervention, the models produce the same overall prevalence of infected individuals in steady state. We consider an intervention that either reduces the contact rate or increases the disease clearance rate. We develop analytical and numerical results characterizing the models and the effects of the intervention. We find that there exist multiple feasible choices of risk stratification, contact distribution, and within- and between-group contact rates for models that stratify risk. We show analytically and empirically that these choices can generate different estimates of intervention effectiveness, and that these differences can be significant enough to alter conclusions from cost-effectiveness analyses and change policy recommendations. We conclude that the choice of how to discretize risk in compartmental epidemic models can influence predicted effectiveness of interventions. Therefore, analysts should examine multiple alternatives and report the range of results.
Project description:Background:Linguists and psychologists have explained the remarkable similarities in the orderings of linguistic elements across languages by suggesting that our inborn ability for language makes available certain innately wired primitives. Different types of adjectives, adverbs, and other elements in the functional spine are considered to occupy fixed positions via innate hierarchies that determine orderings such as A>B>C, banning other permutations (*B>C>A). The goal of this research is to tap into the nature and rigidity of such hierarchies by comparing what happens when people process orderings that either comply with them or violate them. Method:N = 170 neurotypical, adult speakers completed a timed forced choice task that featured stimuli showing a combination of two adjectives and a Spelke-object (e.g., 'I bought a square black table'). Two types of responses were collected: (i) acceptability judgments on a 3-point Likert scale that featured the options 'correct', 'neither correct nor wrong', and 'wrong' and (ii) reaction times. The task featured three conditions: 1. size adjective > nationality adjective, 2. color adjective > shape adjective, 3. subjective comment adjective > material adjective. Each condition had two orders. In the congruent order, the adjective pair was ordered in agreement with what is traditionally accepted as dictated by the universal hierarchy. In the incongruent order, the ordering was reversed, thus the hierarchy was violated. Results:In the first experiment, the results of n = 140 monolinguals showed that across conditions, both congruent and incongruent orders were generally accepted as correct. For 2/3 conditions, the difference in acceptability ratings between congruent and incongruent orders did not reach statistical significance. Using time as a window to processing, reaction times showed that incongruent orders do not take longer to process than congruent ones, as should be the case if the former were treated as being licensed under some type of special condition (e.g., contrastive focus) that reverses the unmarked order and legitimizes the violation of the hierarchy. In the second experiment, the results of n = 30 bidialectals, tested in both language varieties, corroborated the findings of the first experiment. Conclusions:Our findings do not provide evidence for an innate hierarchy for adjective ordering that imposes one rigid, unmarked order. We discuss the importance of notions such as subjectivity and inherentness, and show that for some conditions, not only is there no evidence for a hard constraint that bans incongruent orders, but even simple preferences of congruent orders over incongruent ones are hard to discern. Capturing the bigger picture, given that both the hierarchies and their legit permutations have been described as innate, our results reduce the amount of primitives that are cast as innate, eventually offering a deflationist approach to human linguistic cognition.
Project description:Influenza is an infectious disease that primarily attacks the respiratory system. Innate immunity provides both a very early defense to influenza virus invasion and an effective control of viral growth. Previous modelling studies of virus-innate immune response interactions have focused on infection with a single virus and, while improving our understanding of viral and immune dynamics, have been unable to effectively evaluate the relative feasibility of different hypothesised mechanisms of antiviral immunity. In recent experiments, we have applied consecutive exposures to different virus strains in a ferret model, and demonstrated that viruses differed in their ability to induce a state of temporary immunity or viral interference capable of modifying the infection kinetics of the subsequent exposure. These results imply that virus-induced early immune responses may be responsible for the observed viral hierarchy. Here we introduce and analyse a family of within-host models of re-infection viral kinetics which allow for different viruses to stimulate the innate immune response to different degrees. The proposed models differ in their hypothesised mechanisms of action of the non-specific innate immune response. We compare these alternative models in terms of their abilities to reproduce the re-exposure data. Our results show that 1) a model with viral control mediated solely by a virus-resistant state, as commonly considered in the literature, is not able to reproduce the observed viral hierarchy; 2) the synchronised and desynchronised behaviour of consecutive virus infections is highly dependent upon the interval between primary virus and challenge virus exposures and is consistent with virus-dependent stimulation of the innate immune response. Our study provides the first mechanistic explanation for the recently observed influenza viral hierarchies and demonstrates the importance of understanding the host response to multi-strain viral infections. Re-exposure experiments provide a new paradigm in which to study the immune response to influenza and its role in viral control.
Project description:The process of identifying and modeling functionally divergent subgroups for a specific protein domain class and arranging these subgroups hierarchically has, thus far, largely been done via manual curation. How to accomplish this automatically and optimally is an unsolved statistical and algorithmic problem that is addressed here via Markov chain Monte Carlo sampling. Taking as input a (typically very large) multiple-sequence alignment, the sampler creates and optimizes a hierarchy by adding and deleting leaf nodes, by moving nodes and subtrees up and down the hierarchy, by inserting or deleting internal nodes, and by redefining the sequences and conserved patterns associated with each node. All such operations are based on a probability distribution that models the conserved and divergent patterns defining each subgroup. When we view these patterns as sequence determinants of protein function, each node or subtree in such a hierarchy corresponds to a subgroup of sequences with similar biological properties. The sampler can be applied either de novo or to an existing hierarchy. When applied to 60 protein domains from multiple starting points in this way, it converged on similar solutions with nearly identical log-likelihood ratio scores, suggesting that it typically finds the optimal peak in the posterior probability distribution. Similarities and differences between independently generated, nearly optimal hierarchies for a given domain help distinguish robust from statistically uncertain features. Thus, a future application of the sampler is to provide confidence measures for various features of a domain hierarchy.
Project description:Building fine-grained visual recognition systems that are capable of recognizing tens of thousands of categories, has received much attention in recent years. The well known semantic hierarchical structure of categories and concepts, has been shown to provide a key prior which allows for optimal predictions. The hierarchical organization of various domains and concepts has been subject to extensive research, and led to the development of the WordNet domains hierarchy (Fellbaum, 1998), which was also used to organize the images in the ImageNet (Deng et al., 2009) dataset, in which the category count approaches the human capacity. Still, for the human visual system, the form of the hierarchy must be discovered with minimal use of supervision or innate knowledge. In this work, we propose a new Bayesian generative model for learning such domain hierarchies, based on semantic input. Our model is motivated by the super-subordinate organization of domain labels and concepts that characterizes WordNet, and accounts for several important challenges: maintaining context information when progressing deeper into the hierarchy, learning a coherent semantic concept for each node, and modeling uncertainty in the perception process.
Project description:The wiring of the brain is organized around a putative unimodal-transmodal hierarchy. Here we investigate how this intrinsic hierarchical organization of the brain shapes the transmission of information among regions. The hierarchical positioning of individual regions was quantified by applying diffusion map embedding to resting-state functional MRI networks. Structural networks were reconstructed from diffusion spectrum imaging and topological shortest paths among all brain regions were computed. Sequences of nodes encountered along a path were then labeled by their hierarchical position, tracing out path motifs. We find that the cortical hierarchy guides communication in the network. Specifically, nodes are more likely to forward signals to nodes closer in the hierarchy and cover a range of unimodal and transmodal regions, potentially enriching or diversifying signals en route. We also find evidence of systematic detours, particularly in attention networks, where communication is rerouted. Altogether, the present work highlights how the cortical hierarchy shapes signal exchange and imparts behaviorally relevant communication patterns in brain networks.
Project description:<h4>Background</h4>Many models used in theoretical ecology, or mathematical epidemiology are stochastic, and may also be spatially-explicit. Techniques from quantum field theory have been used before in reaction-diffusion systems, principally to investigate their critical behavior. Here we argue that they make many calculations easier and are a possible starting point for new approximations.<h4>Methodology</h4>We review the many-body field formalism for Markov processes and illustrate how to apply it to a 'Brownian bug' population model, and to an epidemic model. We show how the master equation and the moment hierarchy can both be written in particularly compact forms. The introduction of functional methods allows the systematic computation of the effective action, which gives the dynamics of mean quantities. We obtain the 1-loop approximation to the effective action for general (space-) translation invariant systems, and thus approximations to the non-equilibrium dynamics of the mean fields.<h4>Conclusions</h4>The master equations for spatial stochastic systems normally take a neater form in the many-body field formalism. One can write down the dynamics for generating functional of physically-relevant moments, equivalent to the whole moment hierarchy. The 1-loop dynamics of the mean fields are the same as those of a particular moment-closure.
Project description:Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.