Stochastic epidemics: major outbreaks and the duration of the endemic period

A study is made of a two-dimensional stochastic system that models the spread of an infectious disease in a population. An asymptotic expression is derived for the probability that a major outbreak of the disease will occur in case the number of infectives is small. For the case that a major outbreak has occurred, an asymptotic approximation is derived for the expected time that the disease is in the population. The analytical expressions are obtained by asymptotically solving Dirichlet problems based on the Fokker-Planck equation for the stochastic system. Results of numerical calculations for the analytical expressions are compared with simulation results.     

Dynamic Finite Size Effects in Spiking Neural Networks

We investigate the dynamics of a deterministic finite-sized network of synaptically coupled spiking neurons and present a formalism for computing the network statistics in a perturbative expansion. The small parameter for the expansion is the inverse number of neurons in the network. The network dynamics are fully characterized by a neuron population density that obeys a conservation law analogous to the Klimontovich equation in the kinetic theory of plasmas. The Klimontovich equation does not possess well-behaved solutions but can be recast in terms of a coupled system of well-behaved moment equations, known as a moment hierarchy. The moment hierarchy is impossible to solve but in the mean field limit of an infinite number of neurons, it reduces to a single well-behaved conservation law for the mean neuron density. For a large but finite system, the moment hierarchy can be truncated perturbatively with the inverse system size as a small parameter but the resulting set of reduced moment equations that are still very difficult to solve. However, the entire moment hierarchy can also be re-expressed in terms of a functional probability distribution of the neuron density. The moments can then be computed perturbatively using methods from statistical field theory. Here we derive the complete mean field theory and the lowest order second moment corrections for physiologically relevant quantities. Although we focus on finite-size corrections, our method can be used to compute perturbative expansions in any parameter.     

Development of structure in a society with a dominance relation when new members are added successively

A society with a dominance relation is considered to be built up by starting with a small society and adding new members in succession. As each member is added he engages in contests with each of the older members to determine the dominance relation between them. The probability that the older member dominates is considered to depend on the size of the society and linearly on the older members score. A recurrence relation for the hierarchy index is derived. The approach of the society to a hierarchical structure is considered for various special cases of this probability. Reasonable assumptions concerning this dominance probability are shown to lead to structures close to the hierarchy. If the new member dominates all the older ones below a certain rank, and is dominated by all those above this rank, then the hierarchy will persist if it is the initial structure, or the structure will tend to hierarchy as the size increases, if it is not the initial structure.     

Vocal characteristics of presidential candidates can predict the outcome of actual elections

During political elections, voters rely on various cues that signal good social leadership, such as indicators of physical strength and masculinity. In adult men, masculine traits are related to testosterone levels, and one of those traits is low-pitched voice. Hence, lower pitch in a presidential candidate may be related to the election's outcome. This prediction is supported by experimental evidence showing that people prefer to vote for a candidate with a low-pitched voice. The aim of this study was to investigate the relationship between presidential candidates' vocal characteristics and actual election outcomes in 51 presidential elections held across the world. After analysis of the voices of opposing candidates, results showed that winners had lower-pitched voices with less pitch variability. Moreover, regression analysis revealed an interaction effect of voice pitch and voice pitch variability on the election outcome. Candidates with lower-pitched voices had greater likelihood of winning the election if they had higher pitch variability. This study extends previous findings, shows the importance of assessing vocal characteristics other than voice pitch, and offers external validity for the experimental evidence that candidates' vocal characteristics are related to the election outcome.     

The political gender gap: gender bias in facial inferences that predict voting behavior

Background

Throughout human history, a disproportionate degree of political power around the world has been held by men. Even in democracies where the opportunity to serve in top political positions is available to any individual elected by the majority of their constituents, most of the highest political offices are occupied by male leaders. What psychological factors underlie this political gender gap? Contrary to the notion that people use deliberate, rational strategies when deciding whom to vote for in major political elections, research indicates that people use shallow decision heuristics, such as impressions of competence solely from a candidate''s facial appearance, when deciding whom to vote for. Because gender has previously been shown to affect a number of inferences made from the face, here we investigated the hypothesis that gender of both voter and candidate affects the kinds of facial impressions that predict voting behavior.

Methodology/Principal Finding

Male and female voters judged a series of male and female political candidates on how competent, dominant, attractive and approachable they seemed based on their facial appearance. Then they saw a series of pairs of political candidates and decided which politician they would vote for in a hypothetical election for President of the United States. Results indicate that both gender of voter and candidate affect the kinds of facial impressions that predict voting behavior. All voters are likely to vote for candidates who appear more competent. However, male candidates that appear more approachable and female candidates who appear more attractive are more likely to win votes. In particular, men are more likely to vote for attractive female candidates whereas women are more likely to vote for approachable male candidates.

Conclusions/Significance

Here we reveal gender biases in the intuitive heuristics that voters use when deciding whom to vote for in major political elections. Our findings underscore the impact of gender and physical appearance on shaping voter decision-making and provide novel insight into the psychological foundations underlying the political gender gap.     

On dominance relations and the structure of animal societies: I. Effect of inherent characteristics

Societies are considered in which a non-transitive dominance relation exists between every pair of members, such as the peck-right in a flock of hens. A one-dimensional measure of the structure of such a society,h, is defined, withh=0 for equality andh=1 for the hierarchy. It is assumed that each member of the society is characterized by an ability vector whose components depend on individual characteristics such as size, concentration of sex hormone, etc., but not on social factors such as social rank. The distribution of abilities among members of the society is assumed to be given by a distribution function which is the same for all members, and the probability that one member dominates another is given by a function of the ability vectors of the two. On these assumptions formulas for the expected (mean) value and variance ofh are determined in terms of the distribution and dominance probability functions. Some special cases are calculated, especially that for normany distributed abilities and dominance probability given by the normal probability integral. Several conclusions are derived. If all members are of equal ability, so that dominance probability is 1/2, then any sizable society is much more likely to be near the equality than the hierarchy; and, as the size of the society increases, the probability that it will be near the hierarchy becomes vanishingly small. If the dominance probability is a weighted sum of several independent components, which make up the ability vector, then the society is less likely to be close to the hierarchy as the number of these components increases. The hierarchy is the prevalent structure only if unreasonably small differences in ability are decisive for dominance. From this it appears that the social factors, or psychological factors such as the previous history of dominance, which are not included in the present treatment, may be of great importance in explaining the observed prevalence of structures very close to the hierarchy in flocks of domestic hens.     

On dominance relations and the structure of animal societies: II. Some effects of possible social factors

In a previous paper (Landau, 1951) it was shown that a society with a dominance relation would rarely tend to be close to the hierarchy in structure if dominance is determined solely by the inherent characteristics of the members. Here we consider the effects of other factors, due to social rank or to the outcome of previous encounters which affected dominance. The following results are obtained. A uniform bias against reversal of dominance will have no effect on the stationary distribution of the structure of the society. If the probability of dominance is a linear function of the previously established score (number of members dominated), there will be a small tendency for the society to move toward the hierarchy; but this is negligible for large societies. If a member never challenges another whose score exceeds his own by two or more, or if he can never dominate if he should challenge, then the hierarchy is the only stable structure. From the last result it is concluded that social factors which restrict challenges or the probability of dominance could easily account for societies close to the hierarchy, such as are observed in flocks of domestic hens. The effectiveness of social bias in establishing hierarchies is much greater in small societies than in large ones.     

Body size and food web structure: testing the equiprobability assumption of the cascade model

The cascade model successfuly predicts many patterns in reported food webs. A key assumption of this model is the existence of a predetermined trophic hierarchy; prey are always lower in the hierarchy than their predators. At least three studies have suggested that, in animal food webs, this hierarchy can be explained to a large extent by body size relationships. A second assumption of the standard cascade model is that trophic links not prohibited by the hierarchy occur with equal probability. Using nonparametric contingency table analyses, we tested this ”equiprobability hypothesis” in 16 published animal food webs for which the adult body masses of the species had been estimated. We found that when the hierarchy was based on body size, the equiprobability hypothesis was rejected in favor of an alternative, ”predator-dominance” hypothesis wherein the probability of a trophic link varies with the identity of the predator. Another alternative to equiprobabilty is that the probability of a trophic link depends upon the ratio of the body sizes of the two species. Using nonparametric regression and liklihood ratio tests, we show that a size-ratio based model represents a significant improvement over the cascade model. These results suggest that models with heterogeneous predation probabilities will fit food web data better than the homogeneous cascade model. They also suggest a new way to bridge the gap between static and dynamic food web models. Received: 3 February 1999 / Accepted: 26 October 1999     

Immigrant transit camps ‐ The formation of dependent relations in Israeli society

In this article three approaches to define and explain negative ethnic attitudes are discussed: the anthropology of cultural misunderstanding, the sociology of how differences in group positions are justified ideologically, and the social psychology of maintaining self‐esteem through intergroup differentiation. The‐ aim is to integrate these approaches into an interdisciplinary model. Social identity theory is used as a frame for this integration. The argument developed is that ingroup values are used for intergroup differentiation and evaluation. This leads to the development of stereotypes. Stereotypes reflect misunderstanding, but also anchor social representations of a hierarchy of group positions (ethnic hierarchy). Depending on the ethnic composition of the larger society, majority and minority groups will differ in their ethnic hierarchies. Discrepancies between ethnic hierarchies will lead to ethnic tension. From the perspective developed, a number of hypotheses is derived about how changes in the socio‐economic position of minority groups will affect intergroup evaluations. Hypotheses based on the category differentiation model and the social identity model are specified with respect to the expected changes in stereotypes and intergroup discrimination of the ethnic majority and minority groups.     

Modularity and reliability in the organization of organisms

An organism persists only if it satisfies internal and external constraints. Within the organism networks of processes meet the constraints. In such networks a principle of matching often obtains: the pattern of coupling among processes matches the correlation among constraints. That is, a module—a cluster of coupled processes—meets a constraint. Dissociable modules meet dissociàble constraints. A hierarchy of modules meets a hierarchy of constraints. We have inquired whether such matching is predicted by an optimality criterion in a simple example. We find that in an ensemble of networks with unreliable processes, the networks that meet the constraints with highest reliability obey the principle of matching. The difference in reliability between modular and nonmodular networks that meet the same constraints is a function of the probability of success per process. Our results suggest that this difference is maximal at a probability of success that increases monotonically with the number of processes in the network.     

Stochastic epidemics: the probability of extinction of an infectious disease at the end of a major outbreak

 The aim of this study is to derive an asymptotic expression for the probability that an infectious disease will disappear from a population at the end of a major outbreak (‘fade-out’). The study deals with a stochastic SIR-model. Local asymptotic expansions are constructed for the deterministic trajectories of the corresponding deterministic system, in particular for the deterministic trajectory starting in the saddle point. The analytical expression for the probability of extinction is derived by asymptotically solving a boundary value problem based on the Fokker-Planck equation for the stochastic system. The asymptotic results are compared with results obtained by random walk simulations. Received 20 July 1995; received in revised form 6 May 1996     

The Path Integral Formulation of Climate Dynamics

The chaotic nature of the atmospheric dynamics has stimulated the applications of methods and ideas derived from statistical dynamics. For instance, ensemble systems are used to make weather predictions recently extensive, which are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts since it allows forecasters to issue probabilistic forecasts. These works have modified the dominant paradigm of the interpretation of the evolution of atmospheric flows (and oceanic motions to some extent) attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, which turn out to be the only physical quantity relevant to practice. However, little work has been done on a direct modeling of the probability evolution itself. In this paper it is shown that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows obtaining a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and provides a framework generalizable to red noise, as well as to delaying differential equations, and even field equations, i.e., partial differential equations with noise, for example, general circulation models with noise. These concepts will be applied to an example taken from a simple ENSO model.     

Analysis of longitudinal multinomial outcome data

Analysis of categorical outcomes in a longitudinal study has been an important statistical issue. Continuous outcome in a similar study design is commonly handled by the mixed effects model. The longitudinal binary or Poisson-like outcome analysis is often handled by the generalized estimation equation (GEE) method. Neither method is appropriate for analyzing a multinomial outcome in a longitudinal study, although the cross-sectional multinomial outcome is often analyzed by generalized linear models. One reason that these methods are not used is that the correlation structure of two multinomial variables can not be easily specified. In addition, methods that rely upon GEE or mixed effects models are unsuitable in instances when the focus of a longitudinal study is on the rate of moving from one category to another. In this research, a longitudinal model that has three categories in the outcome variable will be examined. A continuous-time Markov chain model will be used to examine the transition from one category to another. This model permits an unbalanced number of measurements collected on individuals and an uneven duration between pairs of consecutive measurements. In this study, the explicit expression for the transition probability is derived that provides an algebraic form of the likelihood function and hence allows the implementation of the maximum likelihood method. Using this approach, the instantaneous transition rate that is assumed to be a function of the linear combination of independent variables can be estimated. For a comparison between two groups, the odds ratios of occurrence at a particular category and their confidence intervals can be calculated. Empirical studies will be performed to compare the goodness of fit of the proposed method with other available methods. An example will also be used to demonstrate the application of this method.     

THE POWER OF SENSORY DISCRIMINATION METHODS

Difference testing methods are extensively used in a variety of applications from small sensory evaluation tests to large scale consumer tests. A central issue in the use of these tests is their statistical power, or the probability that if a specified difference exists it will be demonstrated as a significant difference in a difference test. A general equation for the power of any discrimination method is given. A general equation for the sample size required to meet Type I and Type II error specifications is also given. Sample size tables for the 2-alternative forced choice (2-AFC), 3-AFC, the duo-trio and the triangular methods are given. Tables of the psychometric functions for the 2-AFC, 3-AFC, triangular and duo-trio methods are also given.     

The degree of intransitivity and its measurement in an assemblage of encrusting cheilostome bryozoa

The outcome of spatial encounters between 12 species of encrusting bryozoans is largely dependent on the angle formed between the direction of growth of the two species. An index has been devised which describes the degree to which the pattern of interspecific overgrowth is an hierarchical, perfectly transitive one, where each species invariably overgrows those beneath it in the hierarchy or an intransitive one, where all of the species have an equal probability of being overgrown; these two states therefore form quantifiable and opposite ends of a continuum. Frontal encounters alone produced a value closer to the transitive end than did encounters from all directions. Since the latter are more likely in nature, the underlying pattern of overgrowth in assemblages of encrusting bryozoans will be a highly intransitive one.     

Stop ‘blaming the man’: perceptions of inequality and opportunities for success in the Obama era among middle-class African Americans

Abstract

This paper builds upon work that has shown that African Americans exhibit a dual consciousness when explaining persistent inequality. We draw upon 45 in-depth interviews with middle-class African Americans following the 2008 election to explore how they explain persistent disadvantage for African Americans, the destigmatization strategies they employ, and the impact they believe the election of Barack Obama will have on opportunities for African Americans. Consistent with dual consciousness theory, we find that respondents explain persistent disadvantage for African Americans by citing structural and motivational factors. We also extend previous work to show that for the majority of respondents the use of individualistic de-stigmatization strategies reinforces their dual consciousness. These respondents are optimistic about Obama's election because it supports their belief that African Americans should assume responsibility for improving their circumstances. A minority of respondents express more concern about the persistence of racial inequality, and consequentially are less optimistic about changes that Obama's election may bring about.     

“The world’s best minority”: Parsis and Hindutva’s ethnic nationalism in India

There is an assumption that nationalist movements which are constituted by an ethnic majority are hostile towards all minorities, so how does one account for such a movement’s affection for one minority and hostility for another? In this paper I explore this question using the case study of a Hindu nationalist movement in India called Hindutva which simultaneously expresses hostility towards Muslims and affection for another minority known as the Parsis. I argue in societies that imagine themselves as plural there is a type of nationalist thought premised upon the existence of both exemplary and threatening minorities. An exemplary minority is imagined as loyal and acculturating, illustrating both how a minority should relate to the majority and why other minorities are threatening. While an historical argument enables the distinction between the majority and minorities, a plural hierarchy of minorities is enabled by mythical stories of coexistence and conflict.     

Density-dependent dispersal in integrodifference equations

Many species exhibit dispersal processes with positive density- dependence. We model this behavior using an integrodifference equation where the individual dispersal probability is a monotone increasing function of local density. We investigate how this dispersal probability affects the spreading speed of a single population and its ability to persist in fragmented habitats. We demonstrate that density-dependent dispersal probability can act as a mechanism for coexistence of otherwise non-coexisting competitors. We show that in time-varying habitats, an intermediate dispersal probability will evolve. Analytically, we find that the spreading speed for the integrodifference equation with density-dependent dispersal probability is not linearly determined. Furthermore, the next-generation operator is not compact and, in general, neither order-preserving nor monotonicity-preserving. We give two explicit examples of non-monotone, discontinuous traveling-wave profiles.      

Social influence in televised election debates: a potential distortion of democracy

A recent innovation in televised election debates is a continuous response measure (commonly referred to as the "worm") that allows viewers to track the response of a sample of undecided voters in real-time. A potential danger of presenting such data is that it may prevent people from making independent evaluations. We report an experiment with 150 participants in which we manipulated the worm and superimposed it on a live broadcast of a UK election debate. The majority of viewers were unaware that the worm had been manipulated, and yet we were able to influence their perception of who won the debate, their choice of preferred prime minister, and their voting intentions. We argue that there is an urgent need to reconsider the simultaneous broadcast of average response data with televised election debates.     

How reproductive allocation and flowering probability of individuals in plant populations are affected by position in stand size hierarchy,plant size and CO2 regime

Aims We investigate the effect of position within a size-structured population on the reproductive allocation (RA) and flowering probability of individual plants of Sinapis arvensis. We also assess the effects of plant size and changing level of CO₂ on both responses.Methods Sinapis arvensis L., (field mustard), an annual agricultural weed, was grown in monoculture at six densities under ambient and elevated CO₂ in a study with 84 stands. Individual aboveground biomass and reproductive biomass were measured. Varying density produced a wide range of mean plant sizes across stands and size hierarchies within stands. Many (~40%) individuals had zero reproductive biomass. Employing a novel modelling approach, we analysed the joint effects of position in stand size hierarchy, plant size and CO₂ on RA and flowering probability of individuals.Important findings We found a strong effect of position within the size hierarchy of individuals in a population: for an individual of a given size, greater size relative to neighbours substantially increased RA and flowering probability at a single harvest time. There was no other effect of plant size on RA. We found a positive effect of elevated CO₂ on RA regardless of position within the size hierarchy. These observed patterns could impact doubly on the reproductive biomass (R) of small individuals. First, because RA is not affected by size, smaller plants will have smaller R than larger plants; and second, for smaller plants lower down in a population size hierarchy, their RA and hence R will be further reduced. These results suggest that size relative to neighbours may be independent of and more important than direct abiotic effects in determining RA. Further studies are required to evaluate how these observed patterns generalize to other populations in non-experimental conditions.