Comprehensive introduction to analysis of continuous and discrete-time signals and systems. Linear time-invariant systems, convolution; Fourier series representations of periodic signals; Continuous ...

Dynamical systems theory continues to offer profound insights into how complex systems evolve over time, with particular focus on the statistical properties that characterise their long‐term behaviour ...

Structures known as 'time crystals' -- which repeat in time as conventional crystals repeat in space -- have recently captured the interest and imagination of researchers across disciplines. The ...

Time crystals break time-translational symmetry rather than spatial symmetry, as ordinary crystals do. Peter Hannaford and Krzysztof Sacha look at how this exotic state could have similar applications ...

Two independent groups of physicists in the US have built what they describe as “time crystals” – systems of interacting particles that are driven by a periodic force but which appear to oscillate ...

At each sampling time instant, one observes system output and action to form discrete-time rewards. The sampled input-output data are collected along the trajectory of the dynamical system in ...

Crystals are nature's most orderly substances. Inside them, atoms and molecules are arranged in regular, repeating structures, giving rise to solids that are stable and rigid—and often beautiful to ...