A neural circuit is a population of neurons interconnected by synapses to carry out a specific function when activated. Neural circuits interconnect to one another to form large scale brain networks. Biological neural networks have inspired the design of artificial neural networks, but artificial neural networks are usually not strict copies of their biological counterparts. Early study Early treatments of neural networks can be found in Herbert Spencer's Principles of Psychology, 3rd edition (1872), Theodor Meynert's Psychiatry (1884), William James' Principles of Psychology (1890), and Sigmund Freud's Project for a Scientific Psychology (composed 1895). The first rule of neuronal learning was described by Hebb in 1949, in the Hebbian theory. Thus, Hebbian pairing of pre-synaptic and post-synaptic activity can substantially alter the dynamic characteristics of the synaptic connection and therefore either facilitate or inhibit signal transmission. In 1959, the neuroscientists, Warren Sturgis McCulloch and Walter Pitts published the first works on the processing of neural networks. They showed theoretically that networks of artificial neurons could implement logical, arithmetic, and symbolic functions. Simplified models of biological neurons were set up, now usually called perceptrons or artificial neurons. These simple models accounted for neural summation (i.e., potentials at the post-synaptic membrane will summate in the cell body). Later models also provided for excitatory and inhibitory synaptic transmission. Connections between neurons The connections between neurons in the brain are much more complex than those of the artificial neurons used in the connectionist neural computing models of artificial neural networks. The basic kinds of connections between neurons are synapses: both chemical and electrical synapses. The establishment of synapses enables the connection of neurons into millions of overlapping, and interlinking neural circuits. Presynaptic proteins called neurexins are central to this process. One principle by which neurons work is neural summation – potentials at the postsynaptic membrane will sum up in the cell body. If the depolarization of the neuron at the axon hillock goes above threshold an action potential will occur that travels down the axon to the terminal endings to transmit a signal to other neurons. Excitatory and inhibitory synaptic transmission is realized mostly by excitatory postsynaptic potentials (EPSPs), and inhibitory postsynaptic potentials (IPSPs). On the electrophysiological level, there are various phenomena which alter the response characteristics of individual synapses (called synaptic plasticity) and individual neurons (intrinsic plasticity). These are often divided into short-term plasticity and long-term plasticity. Long-term synaptic plasticity is often contended