The goal of the inverse problem in electroencephalography is to determine electrical activity within the cranial volume based on potential measurements taken from the scalp. In this paper we discuss the modeling components of our software system for solving the inverse EEG problem. Our implementation is constructed within the BioPSE problem solving environment, a flexible framework for implemen...

Brendt Wohlberg∗, Daniel M. Tartakovsky†, and Marco Dentz‡ ∗Theoretical Division Los Alamos National Laboratory Los Alamos, NM 87545, USA Email: [email protected] †Department of Mechanical and Aerospace Engineering University of California, San Diego La Jolla, CA 92093, USA Email: [email protected] ‡Department of Geosciences Institute of Environmental Assessment and Water Research (IDAEA-CSIC) c/ Jord...

This thesis presents a dynamical system approach to learning forward and inverse models in associative recurrent neural networks. Ambiguous inverse models are represented by multi-stable dynamics. Random projection networks, i.e. reservoirs, together with a rigorous regularization methodology enable robust and efficient training of multi-stable dynamics with application to flexible movement con...

Development of resistance limits efficiency of present anticancer therapies and preventing it remains big challenge in cancer research. It is accepted, at intuitive level, that the resistance emerges as a consequence of cancer cells heterogeneity at molecular, genetic and cellular levels. At the same time, population heterogeneity stands as one of fundamental prerequisite of evolutionary theory...

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated using regression techniques. We propose as regression method a tensor decomposition model that exploits the inherent threeway interaction of positions × veloc...

We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and recently proposed regularization methods, as well as Monte Carlo techniques for Bayesian inference. We classify the inverse methods based on the underlying s...

Mathematical singularities found in the Signal Detection Theory (SDT) based analysis of the 2-Alternative-Forced-Choice (2AFC) method [Katkov, M., Tsodyks, M., & Sagi, D. (2006a). Analysis of two-alternative force-choice Signal Detection Theory model. Journal of Mathematical Psychology, 50, 411-420; Katkov, M., Tsodyks, M., & Sagi, D. (2006b). Singularities in the inverse modeling of 2AFC contr...

Direct quantitative 2-D characterization of sub-50 nm MOSFETs continues to be elusive. This research develops a comprehensive indirect inverse modeling technique for extracting 2-D device topology using combined log(I)-V and C-V data. An optimization loop minimizes the error between a broad range of simulated and measured electrical characteristics by adjusting parame-terized profiles. The extr...

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This paper presents a BRDF modeling method, based on an inverse problem approach. Our method calculates BRDFs to match the appearance of the object specified by the user. By representing BRDFs by a linear combination of basis functions, outgoing radiances of the object surface can be represented using basis functions. The calculation of the desired BRDF results from calculating the correspondin...