energyfield theoriesIt is proven that, using reducible scale invariance at short distances, conformal symmetry implies canonical (Bjorken) scaling, provided diagonal dimensions of dilatation multiplets occuring in the operator product expansion of two electromagnetic currents have the canonical value l n =...
In a quantum theory of gravity, the species scale Λs can be defined as the scale at which corrections to the Einstein action become important or alter
Scale invariance. Let f denote a change of scale function, that is, a linear function of the form \(f(x)=c\,x+d\) with \(c>0\). We use an asterisk to denote the quantities after the scale change on the data. Therefore, we will prove that $$\begin{aligned}\widehat{{\textrm...
In both vertebrates and invertebrates, spatial patterning along the Dorsal-ventral (DV) embryonic axis depends on a morphogen gradient of Bone Morphogenetic Protein signaling. Scale invariance of DV patterning by BMPs has been found in both vertebrates and invertebrates, however the mechanisms that reg...
ofscale-invariance:Ifweusearangesensor–suchasa time-of-flight(TOF)camera[8]–toimagetheobject,we cancomputefeaturesdirectlyonthereconstructedsurface oftheobjectin3Dspace.Inthisway,thefeaturesbecome scale-invariant,becausethe3Dreconstruction–unlikethe imageoftheobject–doesnotundergoscalechangesasthe object...
We describe a technique for computing scale-invariant features on range maps produced by a range sensor, such as a time-of-flight camera. Scale invariance is achieved by computing the features on the reconstructed three-dimensional surface of the object. The technique is general and can be appli...
(arthur.shapiro@ american.edu) Scale-invariance in brightness illusions implicates object-level visual processing Erica Dixon1, Arthur Shapiro1 & Zhong-Lin Lu2 1Department of Psychology American University, Washington, DC, USA, 2Ohio State University, Columbus, OH, USA. Brightness illusions ...
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in terms of scale invariant fields. They correspond to exact scaling ...
The relationship between the magnitude of earthquakes and their spatial and temporal distribution has been observed to exhibit a scale invariance hypothesised to originate from self-organized critical regimes. However, the fractality of earthquake distri
Scale Invariance of the Pi‐space – the Foundation of the Scale‐up Scale-space filtering is one of the hierarchical representations of the waveform in which the given waveform is observed in multiscale measurement. Scale-space filtering using the Gaussian filter, whose bandwidth varies with the ...