Di Francia showed that the number of degrees of freedom in two-dimensional (2-D) monochromatic or incoherent images detected by spatial-bandwidth-limited far-field receivers is approximately equal to the product of the spatial bandwidth of the imaging system and the spatial extent of the object.1 Several researchers have noted that this limit on the information content of imaging fields may be ...

Quantum Chromodynamics (QCD) is the theory of the strong interactions. We review descriptions of hadronic systems motivated by QCD, analyzing the recent controversy between gluonic and bosonic degrees of freedom under the prism of the Cheshire Cat Principle. Our analysis leads to an optimal scheme to study hadronic properties. We proceed to extend this low energy descriptions to the deep inelas...

Studies of the degrees of freedom or “synergies” in musculoskeletal systems rely critically on algorithms to estimate the “dimension” of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are used almost exclusively for this purpose. However, biological systems tend to possess nonlinearities and operate at multiple spatial and temporal scales so that the set ...

We show that in the Maxwell-Lorentz theory of classical electrodynamics most initial values for fields and particles lead to an ill-defined dynamics, as they exhibit singularities or discontinuities along light-cones. This phenomenon suggests Maxwell equations Lorentz force law ought rather be read a system delay differential equations, is, relate function its derivatives at different times. ma...