29 research outputs found

    Taylor series and divisibility

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    On polynomial equations

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    SNNAP: A Tool for Teaching Neuroscience

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    Simulation tools aid in learning neuroscience by providing the student with an interactive environment to carry out simulated experiments and test hypotheses. The field of neuroscience is well suited for the use of simulation tools since nerve cell signaling can be described by mathematical equations and solved by computer. Neural signaling entails the propagation of electrical current along nerve membrane and transmission to neighboring neurons through synaptic connections. Action potentials and synaptic transmission can be simulated and results displayed for visualization and analysis. The neurosimulator SNNAP (Simulator for Neural Networks and Action Potentials) is a simulation environment that provides users with editors for model building, simulator engine and visual display editor. This paper presents several modeling examples that illustrate some of the capabilities and features of SNNAP. First, the Hodgkin-Huxley (HH) model is presented and the threshold phenomenon is illustrated. Second, small neural networks are described with HH models using various synaptic connections available with SNNAP. Synaptic connections may be modulated through facilitation or depression with SNNAP. A study of vesicle pool dynamics is presented using an AMPA receptor model. Finally, a central pattern generator model of the Aplysia feeding circuit is illustrated as an example of a complex network that may be studied with SNNAP. Simulation code is provided for each case study described and tasks are suggested for further investigation

    GEOMETRY, ACTIVITY-DEPENDENT MECHANISMS, MEMBRANE KINETICS AND CHANNEL DENSITY DISTRIBUTION INTERPLAY IN SINGLE NEURON PLASTICITY: A COMPUTATIONAL STUDY

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    Conduction of action potentials throughout the complex morphology of neurons may be modulated in an activity-dependent manner. Among modulatory mechanisms, afterhyperpolarization (AHP) plays an important role. To investigate how the AHP modulatory capabilities on transmission were dependent on the axonal geometry as well as on membrane properties such as channel kinetics, channel density distribution and membrane noise, multi-compartment computational neural models were built, using the neurosimulator SNNAP. Two kinetic schema for the sodium and potassium channels were compared. The simulations suggest that channel kinetics profoundly influence the AHP-dependent modulation of action potential conduction through points of impedance mismatch in the highly branched neurites of neurons

    Computational Model of Touch Sensory Cells (T Cells) of the Leech:Role of the Afterhyperpolarization (AHP) in Activity-Dependent Conduction Failure

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    Abstract. Bursts of spikes in T cells produce an AHP, which results from activation of a Na+/K+ pump and a Ca2+-dependent K+ current. Activity-dependent increases in the AHP are believed to induce conduction block of spikes in several regions of the neuron, which in turn, may decrease presynaptic invasion of spikes and thereby decrease transmitter release. To explore this possibility, we used the neurosimulator SNNAP to develop a multi-compartmental model of the T cell. The model incorporated empirical data that describe the geometry of the cell and activity-dependent changes of the AHP. Simulations indicated that at some branching points, activity-dependent increases of the AHP reduced the number of spikes transmitted from the minor receptive fields to the soma and beyond. More importantly, simulations also suggest that the AHP could modulate, under some circumstances, transmission from the soma to the synaptic terminals, suggesting that the AHP can regulate spike conduction within the presynaptic arborizations of the cell and could in principle contribute to the synaptic depression that is correlated with increases in the AHP

    Bifurcation and Singularity Analysis of a Molecular Network for the Induction of Long-Term Memory

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    Withdrawal reflexes of the mollusk Aplysia exhibit sensitization, a simple form of long-term memory (LTM). Sensitization is due, in part, to long-term facilitation (LTF) of sensorimotor neuron synapses. LTF is induced by the modulatory actions of serotonin (5-HT). Pettigrew et al. developed a computational model of the nonlinear intracellular signaling and gene network that underlies the induction of 5-HT-induced LTF. The model simulated empirical observations that repeated applications of 5-HT induce persistent activation of protein kinase A (PKA) and that this persistent activation requires a suprathreshold exposure of 5-HT. This study extends the analysis of the Pettigrew model by applying bifurcation analysis, singularity theory, and numerical simulation. Using singularity theory, classification diagrams of parameter space were constructed, identifying regions with qualitatively different steady-state behaviors. The graphical representation of these regions illustrates the robustness of these regions to changes in model parameters. Because persistent protein kinase A (PKA) activity correlates with Aplysia LTM, the analysis focuses on a positive feedback loop in the model that tends to maintain PKA activity. In this loop, PKA phosphorylates a transcription factor (TF-1), thereby increasing the expression of an ubiquitin hydrolase (Ap-Uch). Ap-Uch then acts to increase PKA activity, closing the loop. This positive feedback loop manifests multiple, coexisting steady states, or multiplicity, which provides a mechanism for a bistable switch in PKA activity. After the removal of 5-HT, the PKA activity either returns to its basal level (reversible switch) or remains at a high level (irreversible switch). Such an irreversible switch might be a mechanism that contributes to the persistence of LTM. The classification diagrams also identify parameters and processes that might be manipulated, perhaps pharmacologically, to enhance the induction of memory. Rational drug design, to affect complex processes such as memory formation, can benefit from this type of analysis

    Dedekind subrings ofk[x 1,…,x n ] are rings of polynomials

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    Estimating near-surface air temperature across Israel using a machine learning based hybrid approach

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    Rising global temperatures over the last decades have increased heat exposure among populations worldwide. An accurate estimate of the resulting impacts on human health demands temporally explicit and spatially resolved monitoring of near-surface air temperature (Ta). Neither ground-based nor satellite-borne observations can achieve this individually, but the combination of the two provides synergistic opportunities. In this study, we propose a two-stage machine learning-based hybrid model to estimate 1 × 1 km2 gridded intra-daily Ta from surface skin temperature (Ts) across the complex terrain of Israel during 2004–2016. We first applied a random forest (RF) regression model to impute missing Ts from the Moderate Resolution Imaging Spectroradiometer (MODIS) Aqua and Terra satellites, integrating Ts from the geostationary Spinning Enhanced Visible and InfraRed Imager (SEVIRI) satellite and synoptic variables from European Centre for Medium-Range Weather Forecasts' (ECMWF) ERA5 reanalysis data sets. The imputed Ts are in turn fed into the Stage 2 RF-based model to estimate Ta at the satellite overpass hours of each day. We evaluated the model's performance applying out-of-sample fivefold cross validation. Both stages of the hybrid model perform very well with out-of-sample fivefold cross validated R2 of 0.99 and 0.96, MAE of 0.42°C and 1.12°C, and RMSE of 0.65°C and 1.58°C (Stage 1: imputation of Ts, and Stage 2: estimation of Ta from Ts, respectively). The newly proposed model provides excellent computationally efficient estimation of near-surface air temperature at high resolution in both space and time, which helps further minimize exposure misclassification in epidemiological studies
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