Complex-valued Hopfield neural networks extend the classical Hopfield model by allowing neuron activations and synaptic weights to assume complex values. This generalisation enables the encoding of ...

Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

tions of complex numbers to geometry of the straight line and polygon. * He now wishes to extend the theory to the geometry of circles. where r is real. When r = 1 we have, as a special case, the ...

An international team of researchers shows through a concrete theoretical experiment that the prediction by standard complex quantum theory cannot be expressed by its real counterpart and ratifies its ...

A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth ...

Physicists construct theories to describe nature. Let us explain it through an analogy with something that we can do in our everyday life, like going on a hike in the mountains. To avoid getting lost, ...