The generalized sheet transition conditions (GSTCs) are incorporated into a discontinuous Galerkin time-domain (DGTD) method to efficiently simulate metasurfaces. The numerical flux for GSTCs is ...derived for the first time using the Rankine-Hugoniot jump conditions. This numerical flux includes the time derivatives of fields, and therefore, explicit time integration schemes, which are traditionally used with DGTD, do not yield a stable time marching method. To alleviate this bottleneck, a new time marching scheme, which solves a local matrix system for the unknowns of the elements touching the same GSTC face, is developed. This locally implicit method maintains its high-parallel efficiency just like the traditional explicit DGTD schemes. Numerical results, which validate the accuracy of the proposed method against analytical solutions and demonstrate its applicability to the simulation of curved and space/time-varying metasurfaces, are presented.
This paper explores the effects of husbands’ commuting time on wives’ employment and family time allocation. We develop a unitary family model, and we show that when market services are imperfect ...substitutes of home produced goods, a longer husband’s commuting time might decrease his wife’s employment and increase his own working hours. We estimate these effects using employer-induced changes in home-to-work distances. We find that a 1% increase in the husband’s commuting distance reduces his wife’s employment probability by 0.016 percentage points and has a slight positive effect on his own working hours. The effects are stronger for couples with children and for highly educated husbands.
•We study how the husband’s commuting time affects family time allocation.•Theoretically, the effect depends on how household production responds to income.•Husbands’ longer commutes reduce their wives’ employment probability.•Effects are stronger for couples with children and with more educated husbands.•Intra-family interactions are key to understand the overall effect of travel times.
Summary
This article addresses the problem of finite‐time stability (FTS) and finite‐time contractive stability (FTCS) for switched nonlinear time‐delay systems (SNTDSs). By virtues of the ...Lyapunov‐Razumikhin method, Lyapunov functionals approach, and the comparison principle technique, we obtain some improved Razumikhin‐type theorems that verify FTS and FTCS property for SNTDSs. Moreover, our results allow the estimate of the upper bound of the derivatives for Lyapunov functions to be mode dependent functions which can be positive and negative. Meanwhile, the proposed results also improve the related existing results on the same topic by removing some restrictive conditions. Finally, two examples are presented to verify the effectiveness of our methods.
Is time travel just a confusing plot device deployed by science fiction authors and Hollywood filmmakers to amaze and amuse? Or might empirical data prompt a scientific hypothesis of time travel? ...Structured on a fascinating dialogue involving a distinguished physicist, Dr. Rufus, a physics graduate student and a computer scientist this book probes an experimentally supported hypothesis of backwards time travel – and in so doing addresses key metaphysical issues, such as causation, identity over time and free will. The setting is the Jefferson National Laboratory during a period of five days in 2010. Dr. Rufus’s experimental search for the psi-lepton and the resulting intractable data spurs the discussion on time travel. She and her two colleagues are pushed by their observations to address the grandfather paradox and other puzzles about backwards causation, with attention also given to causal loops, multi-dimensional time, and the prospect that only the present exists. Sensible solutions to the main puzzles emerge, ultimately advancing the case for time travel really being possible. A Time Travel Dialogue addresses the possibility of time travel, approaching familiar paradoxes in a rigorous, engaging, and fun manner. It follows in the long philosophical tradition of using dialogue to present philosophical ideas and arguments, but is ground breaking in its use of the dialogue format to introduce readers to the metaphysics of time travel, and is also distinctive in its use of lab results to drive philosophical analysis. The discussion of data that might decide whether time is one-dimensional (one timeline) or multi-dimensional (branching time) is especially novel.
Forecasting of multivariate time series data, for instance the prediction of electricity consumption, solar power production, and polyphonic piano pieces, has numerous valuable applications. However, ...complex and non-linear interdependencies between time steps and series complicate this task. To obtain accurate prediction, it is crucial to model long-term dependency in time series data, which can be achieved by recurrent neural networks (RNNs) with an attention mechanism. The typical attention mechanism reviews the information at each previous time step and selects relevant information to help generate the outputs; however, it fails to capture temporal patterns across multiple time steps. In this paper, we propose using a set of filters to extract time-invariant temporal patterns, similar to transforming time series data into its “frequency domain”. Then we propose a novel attention mechanism to select relevant time series, and use its frequency domain information for multivariate forecasting. We apply the proposed model on several real-world tasks and achieve state-of-the-art performance in almost all of cases. Our source code is available at
https://github.com/gantheory/TPA-LSTM
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Terahertz time-domain spectroscopy (THz-TDS) has shown significant potential in thickness detection. The time-of-flight (TOF) method is most widely used for judgment. However, the method only refers ...to peak information, and waveform information, such as deformation, is simply ignored. Consequently, errors are introduced when testing samples with high dispersion and large absorptive properties. As a result, the signals are broadened, and the peaks become smooth or even disappear, which makes the TOF method fail. In this article, we propose a dispersion compensation (DC) algorithm to solve the above problems. Thickness can be accurately determined by nondispersive signals in the spatial domain. Amplitude compensation is used for materials with large absorption. The DC algorithm's error is less than 1% of the TOF algorithm's error in simulations. While measuring LiNbO<inline-formula> <tex-math notation="LaTeX">_{3}</tex-math> </inline-formula> and water film, errors are, respectively, reduced by 96.24% and 50% compared with using the TOF method, and corresponding deviations are 0.2% and 1.6% compared with the reference thickness. Moreover, the DC algorithm is noniterative, stable, and requires much less calculations than the fitting method. The DC method drastically improves the accuracy by overcoming inherent drawbacks of the TOF method. It can be applied in fields such as nondestructive testing and in-line quality control because of noncontact and real-time advantages.
This study addresses a fixed-time terminal sliding-mode control methodology for a class of second-order non-linear systems in the presence of matched uncertainties and perturbations. A newly defined ...non-singular terminal sliding surface is constructed and a guaranteed closed-loop convergence time independent of initial states is derived based on the phase plane analysis and Lyapunov tools. The simulation results of a single inverted pendulum in the end are included to show the effectiveness of the proposed methodology.
Summary
In this note, the practical fixed‐time stability (PFTS) for discrete‐time impulsive switched nonlinear (DISN) systems is investigated. Firstly, the concept of PFTS is introduced for ...discrete‐time nonlinear (DN) systems, and two sufficient conditions are proposed to verify the PFTS of DN systems by using the positive‐order Lyapunov function. Then, the obtained results are extended to study the PFTS of DISN systems, two stability conditions are given by combining range dwell time and multiple positive‐order Lyapunov functions. Finally, some further discussions on the relaxation of stability conditions are also provided. Two numerical examples are given to illustrate the theoretical results.
Purpose
Lack of control for time‐varying exposures can lead to substantial bias in estimates of treatment effects. The aim of this study is to provide an overview and guidance on some of the ...available methodologies used to address problems related to time‐varying exposure and confounding in pharmacoepidemiology and other observational studies. The methods are explored from a conceptual rather than an analytical perspective.
Methods
The methods described in this study have been identified exploring the literature concerning to the time‐varying exposure concept and basing the search on four fundamental pharmacoepidemiological problems, construction of treatment episodes, time‐varying confounders, cumulative exposure and latency, and treatment switching.
Results
A correct treatment episodes construction is fundamental to avoid bias in treatment effect estimates. Several methods exist to address time‐varying covariates, but the complexity of the most advanced approaches—eg, marginal structural models or structural nested failure time models—and the lack of user‐friendly statistical packages have prevented broader adoption of these methods. Consequently, simpler methods are most commonly used, including, for example, methods without any adjustment strategy and models with time‐varying covariates. The magnitude of exposure needs to be considered and properly modelled.
Conclusions
Further research on the application and implementation of the most complex methods is needed. Because different methods can lead to substantial differences in the treatment effect estimates, the application of several methods and comparison of the results is recommended. Treatment episodes estimation and exposure quantification are key parts in the estimation of treatment effects or associations of interest.
High heterogeneity has been reported among cohort studies investigating the association between metformin and pancreatic cancer survival. Immortal time bias may be one importance source of ...heterogeneity, as it is widely present in previous cohort studies and may severely impair the validity. Our study aimed to examine whether metformin therapy improves pancreatic cancer survival, and to assess the impact of immortal time bias on the effect estimation of metformin in cohort studies. PubMed, EMbase and SciVerse Scopus were searched. Pooled relative risks (RRs) were derived using a random‐effects model. Pooled RR from the six studies without immortal time bias showed no association between metformin and mortality in pancreatic cancer patients (RR 0.93, 95% CI 0.82, 1.05; p = 0.22 and I2 = 75%). In contrast, pooled RR from the nine studies with immortal time bias showed a reduction of 24% in mortality associated with metformin (RR 0.76, 95% CI 0.69, 0.84; p < 0.001 and I2 = 1%). From a meta‐regression model, existence of immortal time bias was associated with a reduction of 18% in the effect estimate of metformin on pancreatic cancer survival (ratio of RR 0.82, 95% CI 0.70, 0.96; p = 0.02). In conclusions, cumulative evidence from cohort studies does not support a beneficial effect of metformin on pancreatic cancer survival. The association between metformin and pancreatic cancer survival has been greatly exaggerated in previous cohort studies due to the wide existence of immortal time bias. More rigorous designs and statistical methods are needed to account for immortal time bias.
What's new?
Metformin is a first‐line drug in the management of type 2 diabetes. More recently, metformin has also been suggested to prolong survival for cancer patients. However, high heterogeneity has been reported among cohort studies investigating pancreatic cancer survival, possibly due to immortal time bias. Here, the authors found that the cumulative evidence from cohort studies does not support a beneficial effect of metformin on pancreatic cancer survival. The association between metformin and pancreatic cancer survival has been greatly exaggerated due to the wide existence of immortal time bias in cohort studies, calling for more rigorous designs and statistical methods.
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