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The story of a neural impulse and what it reveals about how our brains work. We see the last cookie in the box and think, can I take that? We reach a hand out. In the 2.1 seconds that this impulse travels through our brain, billions of neurons communicate with one another, sending blips of voltage through our sensory and motor regions. Neuroscientists call these blips “spikes.” Spikes enable us to do everything: talk, eat, run, see, plan, and decide. In The Spike, Mark Humphries takes readers on the epic journey of a spike through a single, brief reaction. In vivid language, Humphries tells the story of what happens in our brain, what we know about spikes, and what we still have left to understand about them.Drawing on decades of research in neuroscience, Humphries explores how spikes are born, how they are transmitted, and how they lead us to action. He dives into previously unanswered mysteries: Why are most neurons silent? What causes neurons to fire spikes spontaneously, without input from other neurons or the outside world? Why do most spikes fail to reach any destination? Humphries presents a new vision of the brain, one where fundamental computations are carried out by spontaneous spikes that predict what will happen in the world, helping us to perceive, decide, and react quickly enough for our survival.Traversing neuroscience’s expansive terrain, The Spike follows a single electrical response to illuminate how our extraordinary brains work.

Neural transmission. --- Neurosciences. --- Neural sciences --- Neurological sciences --- Neuroscience --- Medical sciences --- Nervous system --- Nerve transmission --- Nervous transmission --- Neurotransmission --- Synaptic transmission --- Transmission of nerve impulses --- Neural circuitry --- Neurophysiology --- Neurotransmitters --- AI. --- Dean Burnett. --- DeepMind. --- Google Brain. --- How Emotions Are Made. --- Lisa Feldman Barrett. --- Matthew Cobb. --- The Idea of the Brain. --- The Idiot Brain. --- action potential. --- artificial intelligence. --- axon. --- basal ganglia. --- brain as a computer. --- brain disorders. --- cognition. --- cognitive. --- connectome. --- connectomics. --- consciousness. --- cortex. --- decision making. --- machine learning. --- motor cortex. --- motor regions. --- neural coding. --- neural computation. --- neural networks. --- predictive brain. --- seeing. --- vision. --- visual cortex.

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Delay, difference, functional, fractional, and partial differential equations have many applications in science and engineering. In this Special Issue, 29 experts co-authored 10 papers dealing with these subjects. A summary of the main points of these papers follows:Several oscillation conditions for a first-order linear differential equation with non-monotone delay are established in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, whereas a sharp oscillation criterion using the notion of slowly varying functions is established in A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay. The approximation of a linear autonomous differential equation with a small delay is considered in Approximation of a Linear Autonomous Differential Equation with Small Delay; the model of infection diseases by Marchuk is studied in Around the Model of Infection Disease: The Cauchy Matrix and Its Properties. Exact solutions to fractional-order Fokker–Planck equations are presented in New Exact Solutions and Conservation Laws to the Fractional-Order Fokker–Planck Equations, and a spectral collocation approach to solving a class of time-fractional stochastic heat equations driven by Brownian motion is constructed in A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise. A finite difference approximation method for a space fractional convection-diffusion model with variable coefficients is proposed in Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients; existence results for a nonlinear fractional difference equation with delay and impulses are established in On Nonlinear Fractional Difference Equation with Delay and Impulses. A complete Noether symmetry analysis of a generalized coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry is provided in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, and new soliton solutions of a fractional Jaulent soliton Miodek system via symmetry analysis are presented in New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis.

Research & information: general --- Mathematics & science --- integro–differential systems --- Cauchy matrix --- exponential stability --- distributed control --- delay differential equation --- ordinary differential equation --- asymptotic equivalence --- approximation --- eigenvalue --- oscillation --- variable delay --- deviating argument --- non-monotone argument --- slowly varying function --- Crank–Nicolson scheme --- Shifted Grünwald–Letnikov approximation --- space fractional convection-diffusion model --- variable coefficients --- stability analysis --- Lane-Emden-Klein-Gordon-Fock system with central symmetry --- Noether symmetries --- conservation laws --- differential equations --- non-monotone delays --- fractional calculus --- stochastic heat equation --- additive noise --- chebyshev polynomials of sixth kind --- error estimate --- fractional difference equations --- delay --- impulses --- existence --- fractional Jaulent-Miodek (JM) system --- fractional logistic function method --- symmetry analysis --- lie point symmetry analysis --- approximate conservation laws --- approximate nonlinear self-adjointness --- perturbed fractional differential equations --- integro–differential systems --- Cauchy matrix --- exponential stability --- distributed control --- delay differential equation --- ordinary differential equation --- asymptotic equivalence --- approximation --- eigenvalue --- oscillation --- variable delay --- deviating argument --- non-monotone argument --- slowly varying function --- Crank–Nicolson scheme --- Shifted Grünwald–Letnikov approximation --- space fractional convection-diffusion model --- variable coefficients --- stability analysis --- Lane-Emden-Klein-Gordon-Fock system with central symmetry --- Noether symmetries --- conservation laws --- differential equations --- non-monotone delays --- fractional calculus --- stochastic heat equation --- additive noise --- chebyshev polynomials of sixth kind --- error estimate --- fractional difference equations --- delay --- impulses --- existence --- fractional Jaulent-Miodek (JM) system --- fractional logistic function method --- symmetry analysis --- lie point symmetry analysis --- approximate conservation laws --- approximate nonlinear self-adjointness --- perturbed fractional differential equations