Mathematical and theoretical biologyMathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.
Neural circuitA neural circuit (also known as a biological neural network BNNs) is a population of neurons interconnected by synapses to carry out a specific function when activated. Multiple neural circuits interconnect with one another to form large scale brain networks. Neural circuits have inspired the design of artificial neural networks, though there are significant differences. 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).
Piecewise linear functionIn mathematics and statistics, a piecewise linear, PL or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. A piecewise linear function is a function defined on a (possibly unbounded) interval of real numbers, such that there is a collection of intervals on each of which the function is an affine function. (Thus "piecewise linear" is actually defined to mean "piecewise affine".
Measure-preserving dynamical systemIn mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most non-dissipative systems) as well as systems in thermodynamic equilibrium.
Recurrent neural networkA recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition.
