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Past, Present and Future of Brain Stimulation

J. Modolo, R. Edwards, J. Campagnaud, B. Bhattacharya, A. Beuter (2010)

Mathematical Modelling of Natural Phenomena

Recent technological advances including brain imaging (higher resolution in space and time), miniaturization of integrated circuits (nanotechnologies), and acceleration of computation speed (Moore’s Law), combined with interpenetration between neuroscience, mathematics, and physics have led to the development of more biologically plausible computational models and novel therapeutic strategies. Today, mathematical models of irreversible medical conditions...

Periodic systems largely system equivalent to periodic discrete-time processes

Osvaldo Maria Grasselli, Sauro Longhi, Antonio Tornambè (2001)

Kybernetika

In this paper, the problem of obtaining a periodic model in state-space form of a linear process that can be modeled by linear difference equations with periodic coefficients is considered. Such a problem was already studied and solved in [r71] on the basis of the notion of system equivalence, but under the assumption that the process has no null characteristic multiplier. In this paper such an assumption is removed in order to generalize the results in [r71] to linear periodic processes with possibly...

Planning identification experiments for cell signaling pathways: An NFκB case study

Krzysztof Fujarewicz (2010)

International Journal of Applied Mathematics and Computer Science

Mathematical modeling of cell signaling pathways has become a very important and challenging problem in recent years. The importance comes from possible applications of obtained models. It may help us to understand phenomena appearing in single cells and cell populations on a molecular level. Furthermore, it may help us with the discovery of new drug therapies. Mathematical models of cell signaling pathways take different forms. The most popular way of mathematical modeling is to use a set of nonlinear...

Plant Growth and Development - Basic Knowledge and Current Views

V. Brukhin, N. Morozova (2010)

Mathematical Modelling of Natural Phenomena

One of the most intriguing questions in life science is how living organisms develop and maintain their predominant form and shape via the cascade of the processes of differentiation starting from the single cell. Mathematical modeling of these developmental processes could be a very important tool to properly describe the complex processes of evolution and geometry of morphogenesis in time and space. Here, we summarize the most important biological knowledge on plant development, exploring the...

Positive and Negative Feedback in Engineering and Biology

E. S. Zeron (2008)

Mathematical Modelling of Natural Phenomena

No other concepts have shaken so deeply the bases of engineering like those of positive and negative feedback. They have played a most prominent role in engineering since the beginning of the previous century. The birth certificate of positive feedback can be traced back to a pair of patents by Edwin H. Armstrong in 1914 and 1922, whereas that of negative feedback is already lost in time. We present in this paper a short review on the feedback's origins in the fields of engineering and biology....

Prescribed performance control of underactuated surface vessels' trajectory using a neural network and integral time-delay sliding mode

Yun Chen, Hua Chen (2023)

Kybernetika

To tackle the underactuated surface vessel (USV) trajectory tracking challenge with input delays and composite disturbances, an integral time-delay sliding mode controller based on backstepping is discussed. First, the law of virtual velocity control is established by coordinate transformation and the position error is caused to converge utilizing the performance function. At the same time, based on the estimation of velocity vector by the high-gain observer (HGO), radial basis function (RBF) neural...

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