An input signal x is filtered by a collection of dilated band-pass wavelets obtained from ψ, followed by a modulus and finally averaged by a dilation of φ. The wavelets we chose decompose the signal in a …

In the context of deriving rotationally invariant representations, the Fourier Transform is particularly appealing since it exhibits invariance to rotational deformations up to phase (a truly invariant …

It is implemented with a deep convolution net-work, which computes successive wavelet transforms and modulus non-linearities. Invariants to scaling, shearing and small deformations are calculated with …

ScatNet [5] cascades wavelet transfor- m with nonlinear modulus and average pooling, to extract a translation invariant feature robust to deformations and preserve high-frequency information for …

As a steerability consistent way of normalizing circular harmonics, we propose to ade-quately normalize their complex modulus. The proper scale follows from k k2 = kRe [ ]k2

For instance, while an individual CNT has an elastic modulus of around 1 TPa, a CNT forest’s compressive elastic modulus are frequently on the order of 1-10 MPa [26], akin to nat-ural rubber.

, Ktx], (7) Here, we note that the text embedding before augmentation [vj mod M, cy] is a concatenation of the prompt embedding vj mod M and the class embedding cy. Recall that M is the number of …

Unlike typical CNNs: 1) regarding the architecture, convolutional layers are defined by fixed wavelet filters, with modulus-based nonlinearity, but without subsequent pooling; 2) regarding the …

The simple geometry of a clamped rod makes it easy to solve for vibration modes analytically as a function of length, diameter, density, and an elastic modulus.

Applying a modulus removes this variability. As a classical result of signal theory, ob-serve also that an averaged rectified signal is approximately equal to the average of its complex envelope [18].