Improved delay‐partitioning approach to robust stability analysis for discrete‐time systems with time‐varying delays and randomly occurring parameter uncertainties

This paper is concerned with the robust stability problem for uncertain discrete‐time systems with interval time‐varying delays and randomly occurring parameter uncertainties. By construction of a suitable Lyapunov–Krasovskii functional and utilization of new zero equalities with delay‐partitioning approach, improved delay‐dependent criteria for the robust stability of the systems are derived in terms of linear matrix inequalities for guaranteeing the asymptotic stability of the concerned systems. The effectiveness and reduction of conservatism of the derived results are demonstrated by three numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust H∞ performance analysis for uncertain discrete‐time singular systems with time‐varying delays

This paper considers the problem of robust H∞ performance analysis for uncertain discrete‐time singular systems with time‐varying delays. Firstly, a delay‐dependent stability criterion under the H∞ performance index for the systems is given based on constructing a generalized Lyapunov–Krasovskii function and introducing a new difference inequality. Then, a sufficient condition ensuing the system to be regular, causal as well as stable for all admissible uncertainties is proposed in terms of a set of strict linear matrix inequalities (LMIs). Finally, we provide examples to show the reduced conservatism and effectiveness of the proposed conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Topological sensitivity analysis for systems biology

Mathematical models of natural systems are abstractions of much more complicated processes. Developing informative and realistic models of such systems typically involves suitable statistical inference methods, domain expertise, and a modicum of luck. Except for cases where physical principles provide sufficient guidance, it will also be generally possible to come up with a large number of potential models that are compatible with a given natural system and any finite amount of data generated from experiments on that system. Here we develop a computational framework to systematically evaluate potentially vast sets of candidate differential equation models in light of experimental and prior knowledge about biological systems. This topological sensitivity analysis enables us to evaluate quantitatively the dependence of model inferences and predictions on the assumed model structures. Failure to consider the impact of structural uncertainty introduces biases into the analysis and potentially gives rise to misleading conclusions.Using simple models to study complex systems has become standard practice in different fields, including systems biology, ecology, and economics. Although we know and accept that such models do not fully capture the complexity of the underlying systems, they can nevertheless provide meaningful predictions and insights (1). A successful model is one that captures the key features of the system while omitting extraneous details that hinder interpretation and understanding. Constructing such a model is usually a nontrivial task involving stages of refinement and improvement.When dealing with models that are (necessarily and by design) gross oversimplifications of the reality they represent, it is important that we are aware of their limitations and do not seek to overinterpret them. This is particularly true when modeling complex systems for which there are only limited or incomplete observations. In such cases, we expect there to be numerous models that would be supported by the observed data, many (perhaps most) of which we may not yet have identified. The literature is awash with papers in which a single model is proposed and fitted to a dataset, and conclusions drawn without any consideration of (i) possible alternative models that might describe the observed behavior and known facts equally well (or even better); or (ii) whether the conclusions drawn from different models (still consistent with current observations) would agree with one another.We propose an approach to assess the impact of uncertainty in model structure on our conclusions. Our approach is distinct from—and complementary to—existing methods designed to address structural uncertainty, including model selection, model averaging, and ensemble modeling (2–9). Analogous to parametric sensitivity analysis (PSA), which assesses the sensitivity of a model’s behavior to changes in parameter values, we consider the sensitivity of a model’s output to changes in its inherent structural assumptions. PSA techniques can usually be classified as (i) local analyses, in which we identify a single “optimal” vector of parameter values, and then quantify the degree to which small perturbations to these values change our conclusions or predictions; or (ii) global analyses, where we consider an ensemble of parameter vectors (e.g., samples from the posterior distribution in the Bayesian formalism) and quantify the corresponding variability in the model’s output. Although several approaches fall within these categories (10–12), all implicitly condition on a particular model architecture. Here we present a method for performing sensitivity analyses for ordinary differential equation (ODE) models where the architecture of these models is not perfectly known, which is likely to be the case for all realistic complex systems. We do this by considering network representations of our models, and assessing the sensitivity of our inferences to the network topology. We refer to our approach as topological sensitivity analysis (TSA).Here we illustrate TSA in the context of parameter inference, but we could also apply our method to study other conclusions drawn from ODE models (e.g., model forecasts or steady-state analyses). When we use experimental data to infer parameters associated with a specific model it is critical to assess the uncertainty associated with our parameter estimates (13), particularly if we wish to relate model parameters to physical (e.g., reaction rate) constants in the real world. Too often this uncertainty is estimated only by considering the variation in a parameter estimate conditional on a particular model, while ignoring the component of uncertainty that stems from potential model misspecification. The latter can, in principle, be considered within model selection or averaging frameworks, where several distinct models are proposed and weighted according to their ability to fit the observed data (2–5). However, the models tend to be limited to a small, often diverse, group that act as exemplars for each competing hypothesis but ignore similar model structures that could represent the same hypotheses. Moreover, we know that model selection results can be sensitive to the particular experiments performed (14).We assume that an initial model, together with parameters or plausible parameter ranges, has been proposed to describe the dynamics of a given system. This model may have been constructed based on expert knowledge of the system, selected from previous studies, or (particularly in the case of large systems) proposed automatically using network inference algorithms (15–19), for example. Using TSA, we aim to identify how reliant any conclusions and inferences are on the particular set of structural assumptions made in this initial candidate model. We do this by identifying alterations to model topology that maintain consistency with the observed dynamics and test how these changes impact the conclusions we draw (Fig. 1). Analogous to PSA we may perform local or global analyses—by testing a small set of “close” models with minor structural changes, or performing large-scale searches of diverse model topologies, respectively. To do this we require efficient techniques for exploring the space of network topologies and, for each topology, inferring the parameters of the corresponding ODE models.Open in a separate windowFig. 1.Overview of TSA applied to parameter inference. (A) Model space includes our initial candidate model and a series of altered topologies that are consistent with our chosen rules (e.g., all two-edge, three-node networks, where nodes indicate species and directed edges show interactions). One topology may correspond to one or several ODE models depending on the parametric forms we choose to represent interactions. (B) We test each ODE model to see whether it can generate dynamics consistent with our candidate model and the available experimental data. For TSA, we select a group of these compatible models and compare the conclusions we would draw using each of them. (C) Associated with each model m is a parameter space Θ_m (gray); using Bayesian methods we can infer the joint posterior parameter distribution (dashed contours) for a particular model and dataset. (D) In some cases, equivalent parameters will be present in several selected models (e.g., θ₁, which is associated with the same interaction in models a–c). We can compare the marginal posterior distribution inferred using each model for a common parameter to test whether our inferences are robust to topological changes, or rely on one specific set of model assumptions (i.e., sensitive). Different models may result in marginal distributions that differ in position and/or shape for equivalent parameters, but we cannot tell from this alone which model better represents reality—this requires model selection approaches (2–4).Even for networks with relatively few nodes (corresponding to ODE models involving few interacting entities), the number of possible topologies can be enormous. Searching this “model space” presents formidable computational challenges. We use here a gradient-matching parameter inference approach that exploits the fact that the nth node, x_n, in our network representation is conditionally independent of all other nodes given its regulating parents, Pa(x_n) (20–26). The exploration of network topologies is then reduced to the much simpler problem of considering, independently for each n, the possible parent sets of x_n in an approach that is straightforwardly parallelized.We use biological examples to illustrate local and global searches of model spaces to identify alternative model structures that are consistent with available data. In some cases we find that even minor structural uncertainty in model topology can render our conclusions—here parameter inferences—unreliable and make PSA results positively misleading. However, other inferences are robust across diverse compatible model structures, allowing us to be more confident in assigning scientific meaning to the inferred parameter values.     

The effect of vitamin D on thyroid autoimmunity in euthyroid men with autoimmune thyroiditis and testosterone deficiency

BackgroundAutoimmune (Hashimoto’s thyroiditis) is characterized by a strong female preponderance, which may suggest that sex hormones have an impact on thyroid autoimmunity. The aim of this study was to investigate whether testosterone determines vitamin D action on thyroid antibody titers and thyroid function tests in men with autoimmune thyroiditis and low testosterone levels.MethodsThe study included 36 men with testosterone deficiency, 17 of whom had been treated for at least 26 weeks with oral testosterone undecanoate (120 mg daily). Because of coexistent euthyroid Hashimoto’s thyroiditis, all participants were then treated with vitamin D (100 μg daily). Serum titers of thyroid peroxidase and thyroglobulin antibodies, serum levels of thyrotropin, free thyroid hormones, testosterone and 25-hydroxyvitamin D, as well as Jostel’s thyrotropin index, SPINA-GT and SPINA-GD were assessed before vitamin D treatment and 26 weeks later.ResultsWith the exception of testosterone levels, there were no significant differences between both study groups in serum hormone levels, antibody titers and thyroid function tests. All participants completed the study. In addition to increasing 25-hydroxyvitamin D levels, vitamin D increased SPINA-GT and reduced thyroid peroxidase and thyroglobulin antibody titers. In testosterone-treated men, vitamin D increased testosterone levels. Vitamin D did not affect serum levels of thyrotropin, free thyroid hormones, Jostel’s thyrotropin index and SPINA-GD. Treatment-induced changes in thyroid antibody titers and SPINA-GT were more pronounced in testosterone-treated than testosterone-naïve men.ConclusionsThe obtained results suggest that the beneficial effect on thyroid autoimmunity and thyroid secretory function is stronger in men receiving testosterone therapy.     

USING MENDELIAN RANDOMISATION TO INFER CAUSALITY IN DEPRESSION AND ANXIETY RESEARCH

Depression and anxiety co‐occur with substance use and abuse at a high rate. Ascertaining whether substance use plays a causal role in depression and anxiety is difficult or impossible with conventional observational epidemiology. Mendelian randomisation uses genetic variants as a proxy for environmental exposures, such as substance use, which can address problems of reverse causation and residual confounding, providing stronger evidence about causality. Genetic variants can be used instead of directly measuring exposure levels, in order to gain an unbiased estimate of the effect of various exposures on depression and anxiety. The suitability of the genetic variant as a proxy can be ascertained by confirming that there is no relationship between variant and outcome in those who do not use the substance. At present, there are suitable instruments for tobacco use, so we use that as a case study. Proof‐of‐principle Mendelian randomisation studies using these variants have found evidence for a causal effect of smoking on body mass index. Two studies have investigated tobacco and depression using this method, but neither found strong evidence that smoking causes depression or anxiety; evidence is more consistent with a self‐medication hypothesis. Mendelian randomisation represents a technique that can aid understanding of exposures that may or may not be causally related to depression and anxiety. As more suitable instruments emerge (including the use of allelic risk scores rather than individual single nucleotide polymorphisms), the effect of other substances can be investigated. Linkage disequilibrium, pleiotropy, and population stratification, which can distort Mendelian randomisation studies, are also discussed.     

Sources of Uncertainty in Intuitive Physics

Recent work suggests that people predict how objects interact in a manner consistent with Newtonian physics, but with additional uncertainty. However, the sources of uncertainty have not been examined. In this study, we measure perceptual noise in initial conditions and stochasticity in the physical model used to make predictions. Participants predicted the trajectory of a moving object through occluded motion and bounces, and we compared their behavior to an ideal observer model. We found that human judgments cannot be captured by simple heuristics and must incorporate noisy dynamics. Moreover, these judgments are biased consistently with a prior expectation on object destinations, suggesting that people use simple expectations about outcomes to compensate for uncertainty about their physical models.     

Robust fault detection filter design for a class of neutral‐type neural networks with time‐varying discrete and unbounded distributed delays

This paper is concerned with the problem of robust fault detection filter design for a class of neutral‐type neural networks with time‐varying discrete and unbounded distributed delays. A Luenberger‐type observer is designed for monitoring fault. By introducing an appropriate Lyapunov–Krasovskii functional and by using Jensen's inequality techniques to deal with its derivative, a new sufficient condition for the existence of robust fault detection filter is proposed in the form of LMIs with nonlinear constraints. To solve the nonlinear problem, a cone complementarity linearization algorithm is proposed. In addition, several numerical examples are provided to illustrate the applicability of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Transitivity performance,relational hierarchy knowledge and awareness: Results of an instructional framing manipulation

The transitive inference (TI) paradigm has been widely used to examine the role of the hippocampus in generalization. Here we consider a surprising feature of experimental findings in this task: the relatively poor transitivity performance and levels of hierarchy knowledge achieved by adult human subjects. We focused on the influence of the task instructions on participants' subsequent performance—a single‐word framing manipulation which either specified the relation between items as transitive (i.e., OLD‐FRAME: choose which item is “older”) or left it ambiguous (i.e., NO‐FRAME: choose which item is “correct”). We show a marked but highly specific effect of manipulating prior knowledge through instruction: transitivity performance and levels of relational hierarchy knowledge were enhanced, but premise performance unchanged. Further, we show that hierarchy recall accuracy, but not conventional awareness scores, was a significant predictor of inferential performance across the entire group of participants. The current study has four main implications: first, our findings establish the importance of the task instructions, and prior knowledge, in the TI paradigm—suggesting that they influence the size of the overall hypothesis space (e.g., to favor a linear hierarchical structure over other possibilities in the OLD‐FRAME). Second, the dissociable effects of the instructional frame on premise and inference performance provide evidence for the operation of distinct underlying mechanisms (i.e., an associative mechanism vs. relational hierarchy knowledge). Third, our findings suggest that a detailed measurement of hierarchy recall accuracy may be a more sensitive index of relational hierarchy knowledge, than conventional awareness score—and should be used in future studies investigating links between awareness and inferential performance. Finally, our study motivates an experimental setting that ensures robust hierarchy learning across participants—therefore facilitating study of the neural mechanisms underlying the learning and representation of linear hierarchies. © 2013 The Authors. Hippocampus Published by Wiley Periodicals, Inc.     

A comparison of synthetic control approaches for the evaluation of policy interventions using observational data: Evaluating the impact of redesigning urgent and emergency care in Northumberland

Objective

To compare the original synthetic control (OSC) method with alternative approaches (Generalized [GSC], Micro [MSC], and Bayesian [BSC] synthetic control methods) and re-evaluate the impact of a significant restructuring of urgent and emergency care in Northeast England, which included the opening of the UK's first purpose-built specialist emergency care hospital.

Data Sources

Simulations and data from Secondary Uses Service data, a single comprehensive repository for patient-level health care data in England.

Study Design

Hospital use of individuals exposed and unexposed to the restructuring is compared. We estimate the impact using OSC, MSC, BSC, and GSC applied at the general practice level. We contrast the estimation methods' performance in a Monte Carlo simulation study.

Data Collection/Extraction Methods

Hospital activity data from Secondary Uses Service for patients aged over 18 years registered at a general practice in England from April 2011 to March 2019.

Principal Findings

None of the methods dominated all simulation scenarios. GSC was generally preferred. In contrast to an earlier evaluation that used OSC, GSC reported a smaller impact of the opening of the hospital on Accident and Emergency (A&E) department (also known as emergency department or casualty) visits and no evidence for any impact on the proportion of A&E patients seen within 4 h.

Conclusions

The simulation study highlights cases where the considered methods may lead to biased estimates in health policy evaluations. GSC was found to be the most reliable method of those considered. Considering more disaggregated data over a longer time span and applying GSC indicates that the specialist emergency care hospitals in Northumbria had less impact on A&E visits and waiting times than suggested by the original evaluation which applied OSC to more aggregated data.     

Application of adaptive neuro-fuzzy inference system for epileptic seizure detection using wavelet feature extraction

Intelligent computing tools such as artificial neural network (ANN) and fuzzy logic approaches are demonstrated to be competent when applied individually to a variety of problems. Recently, there has been a growing interest in combining both these approaches, and as a result, neuro-fuzzy computing techniques have been evolved. In this study, a new approach based on an adaptive neuro-fuzzy inference system (ANFIS) was presented for epileptic seizure detection. The proposed ANFIS model combined the neural network adaptive capabilities and the fuzzy logic qualitative approach. Decision making was performed in two stages: feature extraction using the wavelet transform (WT) and the ANFIS trained with the backpropagation gradient descent method in combination with the least squares method. Some conclusions concerning the impacts of features on the detection of epileptic seizures were obtained through analysis of the ANFIS. The results are highly promising, and a comparative analysis suggests that the proposed modeling approach outperforms ANN model in terms of training performances and classification accuracies. The results confirmed that the proposed ANFIS model has some potential in epileptic seizure detection. The ANFIS model achieved accuracy rates which were higher than that of the stand-alone neural network model.