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Computational Modeling of Neural Systems

Programming Biologically Realistic Simulations With Python

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Unlock the secrets of the brain with "Computational Modeling of Neural Systems: Programming Biologically Realistic Simulations." This comprehensive guide immerses you in the world of neural simulations, providing you with the tools and knowledge to create biologically realistic models using Python. Key Features * Comprehensive exploration of prominent neural models and theories. * Step-by-step Python implementations for each model and concept. * Covers both theoretical foundations and practical applications. * Ideal for students, researchers, and professionals in computational neuroscience, AI, and machine learning. * Detailed explanations of complex mathematical concepts made accessible. Book Description Delve into the intricacies of neural modeling with this extensive resource, designed to equip you with the skills to simulate neural system dynamics accurately. From fundamental neuron models like Hodgkin-Huxley and FitzHugh-Nagumo to advanced topics in machine learning and Bayesian data analysis, this book spans an impressive array of computational techniques. Harness the power of Python to implement models and drive innovations at the intersection of neuroscience and technology. Elevate your understanding of neural coding, synchronization, plasticity, and more through this meticulously crafted guide. What You Will Learn * Discover the ionic mechanisms behind neuronal action potentials with Hodgkin-Huxley equations. * Simplify neuronal excitability using the FitzHugh-Nagumo two-variable system. * Utilize the Morris-Lecar model to capture oscillatory neural behaviors with calcium dynamics. * Master the mathematical abstraction of neuronal firing via the integrate-and-fire model. * Extend neuronal firing simulations with the Leaky Integrate-and-Fire model. * Synthesize computational efficiency and realism using the Izhikevich neuron model. * Model population dynamics with Wilson-Cowan equations for excitatory and inhibitory neurons. * Apply the cable equation for dendritic voltage distribution in neurons. * Integrate complex dendritic morphologies using Rall's dendritic cable model. * Incorporate synaptic inputs with conductance models for realistic simulations. * Implement Hebbian learning rules to model synaptic plasticity mathematically. * Explore spike-timing-dependent plasticity (STDP) with temporal kernel models. * Examine Bienenstock-Cooper-Munro (BCM) theory and its sliding threshold mechanism. * Model synaptic facilitation and depression with dynamical systems. * Analyze recurrent Hopfield networks for memory storage as attractor states. * Study Boltzmann machines for energy-efficient unsupervised learning. * Implement liquid state machines to harness transient dynamics for computational tasks. * Utilize echo state networks for time series data processing with fixed recurrent dynamics. * Apply dynamic causal modeling for neural connectivity inference using Bayesian methods. * Simplify large-scale neural networks with mean-field approximation techniques. * Use the Fokker-Planck equation to describe neuronal state probability densities. * Model ion channel kinetics and synaptic states using Markov processes. * Quantify information transmission in neural coding with information theory concepts. * Decode neural signals with optimal estimation using Kalman filters. * Introduce variability in neuronal responses with stochastic differential equations. * Analyze synchronization phenomena in neural networks with the Kuramoto model. * Explore synchronization and stability in coupled oscillator models within neural networks. * Represent binary neurons using the Ising model for phase transitions and system dynamics.

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