Browsing Mathematics by Title
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Computation of the response functions of spiral waves in active media
(American Physical Society, 2009)Rotating spiral waves are a form of selforganization observed in spatially extended systems of physical, chemical, and biological natures. A small perturbation causes gradual change in spatial location of spiral's rotation ... 
A computational biomarker of idiopathic generalized epilepsy from resting state EEG
(Wiley, 20160808)Epilepsy is one of the commonest serious neurological conditions. It is characterized by the tendency to have recurrent seizures, which arise against a backdrop of apparently normal brain activity. At present, clinical ... 
A computational investigation of the finitetime blowup of the 3D incompressible Euler equations based on the Voigt regularization
(American Physical Society, 201512)We report the results of a computational investigation of two recently proved blowup criteria for the 3D incompressible Euler equations. These criteria are based on an inviscid regularization of the Euler equations known ... 
A computational study of stimulus driven epileptic seizure abatement
(Public Library of Science, 20141222)Active brain stimulation to abate epileptic seizures has shown mixed success. In spikewave (SW) seizures, where the seizure and background state were proposed to coexist, singlepulse stimulations have been suggested to ... 
A Computer Simulation Study of Anatomy Induced Drift of Spiral Waves in the Human Atrium
(Hindawi Publishing Corporation, 2014)The interaction of spiral waves of excitation with atrial anatomy remains unclear. This simulation study isolates the role of atrial anatomical structures on spiral wave spontaneous drift in the human atrium. We implemented ... 
Conditions for propagation and block of excitation in an asymptotic model of atrial tissue.
(2006)Detailed ionic models of cardiac cells are difficult for numerical simulations because they consist of a large number of equations and contain small parameters. The presence of small parameters, however, may be used for ... 
Conditions for sinktosource transitions and runaway feedbacks from the land carbon cycle
(Cambridge University Press, 200602)The first GCM climatecarbon cycle simulation indicated that the land biosphere could provide a significant acceleration of 21st century climate change (Cox et al. 2000). In this numerical experiment the carbon storage was ... 
Cone exchange transformations and boundedness of orbits
(Cambridge University Press, 2010)We introduce a class of twodimensional piecewise isometries on the plane that we refer to as cone exchange transformations (CETs). These are generalizations of interval exchange transformations (IETs) to 2D unbounded ... 
Confidence in Classification: A Bayesian Approach
(Springer Verlag, 2006)Bayesian classification is currently of considerable interest. It provides a strategy for eliminating the uncertainty associated with a particular choice of classifiermodel parameters, and is the optimal decisiontheoretic ... 
Confident interpretation of Bayesian decision tree ensembles for clinical applications
(Institute of Electrical and Electronics Engineers (IEEE), 2007)Bayesian averaging (BA) over ensembles of decision models allows evaluation of the uncertainty of decisions that is of crucial importance for safetycritical applications such as medical diagnostics. The interpretability ... 
A conjecture of Stanley on alternating permutations
(Electronic Journal of Combinatorics, 2007)We give two simple proofs of a conjecture of Richard Stanley concerning the equidistribution of derangements and alternating permutations with the maximal number of fixed points. 
Contextdependent interaction leads to emergent search behavior in social aggregates
(National Academy of Sciences, 2009)Locating the source of an advected chemical signal is a common challenge facing many living organisms. When the advecting medium is characterized by either high Reynolds number or high Peclet number, the task becomes highly ... 
Continuationbased numerical detection of afterdepolarization and spikeadding thresholds.
(Massachusetts Institute of Technology Press (MIT Press), 20130311)The changes in neuronal firing pattern are signatures of brain function, and it is of interest to understand how such changes evolve as a function of neuronal biophysical properties. We address this important problem by ... 
Control of Ca2+ Influx and Calmodulin Activation by SKChannels in Dendritic Spines
(Public Library of Science, 20160527)The key trigger for Hebbian synaptic plasticity is influx of Ca2+ into postsynaptic dendritic spines. The magnitude of [Ca2+] increase caused by NMDAreceptor (NMDAR) and voltagegated Ca2+ channel (VGCC) activation is ... 
Control of Ca2+ influx and calmodulin activation by SKchannels in dendritic spines (dataset)
(PLoS, 20160505)The key trigger for Hebbian synaptic plasticity is influx of Ca2+ into postsynaptic dendritic spines. The magnitude of [Ca2+] increase caused by NMDAreceptor (NMDAR) and voltagegated Ca2+ channel (VGCC) activation is ... 
Control of scrollwave turbulence using resonant perturbations
(American Physical Society, 2008)Turbulence of scroll waves is a sort of spatiotemporal chaos that exists in threedimensional excitable media. Cardiac tissue and the BelousovZhabotinsky reaction are examples of such media. In cardiac tissue, chaotic ... 
Controlbased continuation of unstable periodic orbits
(American Society of Mechanical Engineers (ASME), 2011)We present an experimental procedure to track periodic orbits through a fold (saddlenode) bifurcation and demonstrate it with a parametrically excited pendulum experiment where the tracking parameter is the amplitude of ... 
Controlling unstable chaos: stabilizing chimera states by feedback
(American Physical Society, 2014)We present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a ... 
Controls on terrestrial carbon feedbacks by productivity versus turnover in the CMIP5 Earth System Models
(European Geosciences Union (EGU), 20150907)© Author(s) 2015. To better understand sources of uncertainty in projections of terrestrial carbon cycle feedbacks, we present an approach to separate the controls on modeled carbon changes. We separate carbon changes into ... 
Convergence to local random attractors
(Taylor & Francis, 2003)Random attractors allow one to classify qualitative and quantitative aspects of the longtime behaviour of stochastically forced systems viewed as random dynamical systems (RDS) in an analogous way to attractors for ...