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Deterministische Modelle aus Evolutionsbiologie, Populationsgenetik und Epidemiologie
Techniques in Engineering Sciences
Theoretical Advances and Advanced Applications

Abstract

In this work, the effectiveness of the adaptive neural based fuzzy inference system (ANFIS) in identifying underactuated systems is illustrated. Two case studies of underactuated systems are used to validate the system identification i. e., linear inverted pendulum (LIP) and rotary inverted pendulum (RIP). Both the systems are treated as benchmark systems in modeling and control theory for their inherit nonlinear, unstable, and underactuated behavior. The systems are modeled with ANFIS using the input-output data acquired from the dynamic response of the nonlinear analytical model of the systems. The dynamic response of the ANFIS model is simulated and compared to the nonlinear mathematical model of the inverted pendulum systems. In order to check the effectiveness of the ANFIS model, mean square error is used as the performance index. From the obtained simulation results, it has been perceived that the ANFIS model performed satisfactorily within the trained operating range while a minor deviation is seen outside the trained operating region for both the case studies. Furthermore, the experimental validation of the of the proposed ANFIS model is done by comparing it with the experimental model of the rotary inverted pendulum. The obtained results show that the response of ANFIS model is in close agreement to the experimental model of the rotary inverted pendulum.

Abstract

We study a system of particles in a two-dimensional geometry that move according to a reinforced random walk with transition probabilities dependent on the solutions of reaction-diffusion equations (RDEs) for the underlying fields. A birth process and a history-dependent killing process are also considered. This system models tumor-induced angiogenesis, the process of formation of blood vessels induced by a growth factor (GF) released by a tumor. Particles represent vessel tip cells, whose trajectories constitute the growing vessel network. New vessels appear and may fuse with existing ones during their evolution. Thus, the system is described by tracking the density of active tips, calculated as an ensemble average over many realizations of the stochastic process. Such density satisfies a novel discrete master equation with source and sink terms. The sink term is proportional to a space-dependent and suitably fitted killing coefficient. Results are illustrated studying two influential angiogenesis models.

Abstract

In recent years, more and more people are applying Convolutional Neural Networks to the study of sound signals. The main reason is the translational invariance of convolution in time and space. Thereby the diversity of the sound signal can be overcome. However, in terms of sound direction recognition, there are also problems such as a microphone matrix being too large, and feature selection. This paper proposes a sound direction recognition using a simulated human head with microphones at both ears. Theoretically, the two microphones cannot distinguish the front and rear directions. However, we use the original data of the two channels as the input of the convolutional neural network, and the resolution effect can reach more than 0.9. For comparison, we also chose the delay feature (GCC) for sound direction recognition. Finally, we also conducted experiments that used probability distributions to identify more directions.

Abstract

This paper studies capital mobility in commodity-exporting economies. These countries substantially depend on world commodity prices and have rather high level of savings on average, so it is naturally to assume that they demonstrate special patterns of capital mobility. Our main hypothesis is that constraints on capital mobility in this group of countries depend upon the level of savings compared to the level of investments. In particular, with high savings that follow higher world demand and higher commodity prices, financing country’s desirable level of investment is not a big deal. At the same time, in the case of negative terms of trade shocks these commodity-exporting economies may experience lower savings and higher country risk-premium. This may lead to restrictions on borrowing capital in the global market, resulting in a high correlation between investments and savings. The results of threshold regressions speak in favour of our hypothesis.

Abstract

Log-linear models are popular in practice because the slope of a log-transformed regressor is believed to give an unit-free elasticity. This widely held belief is, however, not true if the model error term has a heteroskedasticity function that depends on the regressor. This paper examines various mean – and quantile-based elasticities (mean of elasticity, elasticity of conditional mean, quantile of elasticity, and elasticity of conditional quantile) to show under what conditions these are equal to the slope of a log-transformed regressor. A particular attention is given to the ‘elasticity of conditional mean (i.e., regression function)’, which is what most researchers have in mind when they use log-linear models, and we provide practical ways to find it in the presence of heteroskedasticity. We also examine elasticities in exponential models which are closely related to log-linear models. An empirical illustration for health expenditure elasticity with respect to income is provided to demonstrate our main findings.

Abstract

This study examines whether threshold models allow to better understand the dynamic relationship between spot and futures prices for crude oil and natural gas. Our findings are threefold. First, we show that the futures curve delivers relatively accurate forecasts for energy commodity prices. Second, we provide evidence that the relationship between spot and futures prices is regime dependent but accounting for this property does not improve the quality of out-of-sample forecasts. Third, we demonstrate that using information on the dynamics of financial variables (exchange rates, stock and uncertainty indices, interest rates or industrial and precious metal prices) does not contribute to the quality of futures-based forecasts. This suggests that the predictive content of these variables is already contained in futures prices.