Noise Induced Coherence in Neural Networks

We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in the thermodynamic limit ($N\to \infty$) a broadband peak and an additional delta-function peak that is absent from the powerspectrum of an isolated element. The powerspectrum of the mean output signal only exhibits the delta-function peak. These results are explained analytically in an exactly soluble oscillator model with global phase coupling.Comment: 4 pages ReVTeX and 3 postscript figure

New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. II

In the first part of this paper math-ph/0612078, a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained in math-ph/0612078 but not vise versa. In the second part the symmetries obtained in are successfully applied for constructing exact solutions of the relevant equations. In the particular case, new exact solutions of nonlinear reaction-diffusion-convection (RDC) equations arising in application and their natural generalizations are found

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.Comment: 22 pages, 3 figures, 2 table

The Science of Phylogenetic Systematics: Explanation, Prediction, and Test

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73926/1/j.1096-0031.1999.tb00279.x.pd

Fully-Coupled Electromechanical Simulations of the LV Dog Anatomy Using HPC: Model Testing and Verification

Verification of electro-mechanic models of the heart require a good amount of reliable, high resolution, thorough in-vivo measurements. The detail of the mathematical models used to create simulations of the heart beat vary greatly. Generally, the objective of the simulation determines the modeling approach. However, it is important to exactly quantify the amount of error between the various approaches that can be used to simulate a heart beat by comparing them to ground truth data. The more detailed the model is, the more computing power it requires, we therefore employ a high-performance computing solver throughout this study. We aim to compare models to data measured experimentally to identify the effect of using a mathematical model of fibre orientation versus the measured fibre orientations using DT-MRI. We also use simultaneous endocardial stimuli vs an instantaneous myocardial stimulation to trigger the mechanic contraction. Our results show that synchronisation of the electrical and mechanical events in the heart beat are necessary to create a physiological timing of hemodynamic events. Synchronous activation of all of the myocardium provides an unrealistic timing of hemodynamic events in the cardiac cycle. Results also show the need of establishing a protocol to quantify the zero-pressure configuration of the left ventricular geometry to initiate the simulation protocol; however, the predicted zero-pressure configuration of the same geometry was different, depending on the origin of the fibre field employed.This work has been done with the support of the grant SEV-2011-00067 of Severo Ochoa Program, awarded by the Spanish Government to the Barcelona Supercomputing Center. Part of the research leading to these results has received funding from the Seventh Framework Programme (FP7/2007-2013) under grant agreement n 611823. It has also been partially funded from the by the Spanish Ministry of Economy and Competitiveness (TIN2011-28067).Peer ReviewedPostprint (author's final draft

Analytically Solvable Asymptotic Model of Atrial Excitability

We report a three-variable simplified model of excitation fronts in human atrial tissue. The model is derived by novel asymptotic techniques \new{from the biophysically realistic model of Courtemanche et al (1998) in extension of our previous similar models. An iterative analytical solution of the model is presented which is in excellent quantitative agreement with the realistic model. It opens new possibilities for analytical studies as well as for efficient numerical simulation of this and other cardiac models of similar structure

Radiocarbon dating and cultural dynamics across Mongolia’s early pastoral transition

All necessary permits were obtained for the described study, which complied with all relevant regulations. Collaboration contract between the Max Planck Institute for the Science of Human HIstory and the National University of Mongolia began on the 10th November, 2016. Export number 10/413 (7b/52) was received on the 2nd Feb, 2017 (#A0109258, MN DE 7 643). This research was supported by the Max Planck Institute for the Science of Human History. Special thanks to Dr. Katerina Douka and the Oxford Radiocarbon Accelerator Laboratory for conducting 14C analysis, and to all of the original excavators and authors who published the radiocarbon dates cited in this study.Peer reviewedPublisher PD