Generalized Theorems for Nonlinear State Space Reconstruction

Takens' theorem (1981) shows how lagged variables of a single time series can be used as proxy variables to reconstruct an attractor for an underlying dynamic process. State space reconstruction (SSR) from single time series has been a powerful approach for the analysis of the complex, non-linear systems that appear ubiquitous in the natural and human world. The main shortcoming of these methods is the phenomenological nature of attractor reconstructions. Moreover, applied studies show that these single time series reconstructions can often be improved ad hoc by including multiple dynamically coupled time series in the reconstructions, to provide a more mechanistic model. Here we provide three analytical proofs that add to the growing literature to generalize Takens' work and that demonstrate how multiple time series can be used in attractor reconstructions. These expanded results (Takens' theorem is a special case) apply to a wide variety of natural systems having parallel time series observations for variables believed to be related to the same dynamic manifold. The potential information leverage provided by multiple embeddings created from different combinations of variables (and their lags) can pave the way for new applied techniques to exploit the time-limited, but parallel observations of natural systems, such as coupled ecological systems, geophysical systems, and financial systems. This paper aims to justify and help open this potential growth area for SSR applications in the natural sciences

Quantifying the behavior of stock correlations under market stress

Understanding correlations in complex systems is crucial in the face of turbulence, such as the ongoing financial crisis. However, in complex systems, such as financial systems, correlations are not constant but instead vary in time. Here we address the question of quantifying state-dependent correlations in stock markets. Reliable estimates of correlations are absolutely necessary to protect a portfolio. We analyze 72 years of daily closing prices of the 30 stocks forming the Dow Jones Industrial Average (DJIA). We find the striking result that the average correlation among these stocks scales linearly with market stress reflected by normalized DJIA index returns on various time scales. Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed. Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios

Early Warning Signals for Critical Transitions: A Generalized Modeling Approach

Critical transitions are sudden, often irreversible, changes that can occur in a large variety of complex systems; signals that warn of critical transitions are therefore highly desirable. We propose a new method for early warning signals that integrates multiple sources of information and data about the system through the framework of a generalized model. We demonstrate our proposed approach through several examples, including a previously published fisheries model. We regard our method as complementary to existing early warning signals, taking an approach of intermediate complexity between model-free approaches and fully parameterized simulations. One potential advantage of our approach is that, under appropriate conditions, it may reduce the amount of time series data required for a robust early warning signal

Negative phenotypic and genetic associations between copulation duration and longevity in male seed beetles

Reproduction can be costly and is predicted to trade-off against other characters. However, while these trade-offs are well documented for females, there has been less focus on aspects of male reproduction. Furthermore, those studies that have looked at males typically only investigate phenotypic associations, with the underlying genetics often ignored. Here, we report on phenotypic and genetic trade-offs in male reproductive effort in the seed beetle, Callosobruchus maculatus. We find that the duration of a male's first copulation is negatively associated with subsequent male survival, phenotypically and genetically. Our results are consistent with life-history theory and suggest that like females, males trade-off reproductive effort against longevity

Validation of Agent-Based Models in Economics and Finance

Since the survey by Windrum et al. (Journal of Artificial Societies and Social Simulation 10:8, 2007), research on empirical validation of agent-based models in economics has made substantial advances, thanks to a constant flow of high-quality contributions. This Chapter attempts to take stock of such recent literature to offer an updated critical review of the existing validation techniques. We sketch a simple theoretical framework that conceptualizes existing validation approaches, which we examine along three different dimensions: (i) comparison between artificial and real-world data; (ii) calibration and estimation of model parameters; and (iii) parameter space exploration. Finally, we discuss open issues in the field of ABM validation and estimation. In particular, we argue that more research efforts should be devoted toward advancing hypothesis testing in ABM, with specific emphasis on model stationarity and ergodicity

Knee-clicks and visual traits indicate fighting ability in eland antelopes: multiple messages and back-up signals

Abstract Background Given the costs of signalling, why do males often advertise their fighting ability to rivals using several signals rather than just one? Multiple signalling theories have developed largely in studies of sexual signals, and less is known about their applicability to intra-sexual communication. We here investigate the evolutionary basis for the intricate agonistic signalling system in eland antelopes, paying particular attention to the evolutionary phenomenon of loud knee-clicking. Results A principal components analysis separated seven male traits into three groups. The dominant frequency of the knee-clicking sound honestly indicated body size, a main determinant of fighting ability. In contrast, the dewlap size increased with estimated age rather than body size, suggesting that, by magnifying the silhouette of older bulls disproportionately, the dewlap acts as an indicator of age-related traits such as fighting experience. Facemask darkness, frontal hairbrush size and body greyness aligned with a third underlying variable, presumed to be androgen-related aggression. A longitudinal study provided independent support of these findings. Conclusion The results show that the multiple agonistic signals in eland reflect three separate components of fighting ability: (1) body size, (2) age and (3) presumably androgen-related aggression, which is reflected in three backup signals. The study highlights how complex agonistic signalling systems can evolve through the simultaneous action of several selective forces, each of which favours multiple signals. Specifically, loud knee-clicking is discovered to be an honest signal of body size, providing an exceptional example of the potential for non-vocal acoustic communication in mammals.</p

Implementing mentor mothers in family practice to support abused mothers: Study protocol

Contains fulltext : 97988.pdf (postprint version ) (Open Access)ABSTRACT: BACKGROUND: Intimate partner violence is highly prevalent and mostly affects women with negative consequences for their physical and mental health. Children often witness the violence which has negative consequences for their well-being too. Care offered by family physicians is often rejected because abused women experience a too high threshold. Mentor mother support, a low threshold intervention for abused mothers in family practice, proved to be feasible and effective in Rotterdam, the Netherlands. The primary aim of this study is to investigate which factors facilitate or hinder the implementation of mentor mother support in family practice. Besides we evaluate the effect of mentor mother support in a different region. METHODS/DESIGN: An observational study with pre- and posttests will be performed. Mothers with home living children or pregnant women who are victims of intimate partner violence will be offered mentor mother support by the participating family physicians. The implementation process evaluation consists of focus groups, interviews and questionnaires. In the effect evaluation intimate partner violence, the general health of the abused mother, the mother-child relationship, social support, and acceptance of professional help will be measured twice (t = 0 and t = 6 months) by questionnaires, reporting forms, medical records and interviews with the abused mothers. Qualitative coding will be used to analyze the data from the reporting forms, medical records, focus groups, interviews, and questionnaires. Quantitative data will be analyzed with descriptive statistics, chi square test and t-test matched pairs. DISCUSSION: While other intervention studies only evaluate the feasibility and effectiveness of the intervention, our primary aim is to evaluate the implementation process and thereby investigate which factors facilitate or hinder implementation of mentor mother support in family practice.6 p