Related papers: On the Shiftability of Dual-Tree Complex Wavelet T…
While insights into the workings of the transformer model have largely emerged by analysing their behaviour on language tasks, this work investigates the representations learnt by the Vision Transformer (ViT) encoder through the lens of…
The Hilbert transform (HT) and associated Gabor analytic signal (GAS) representation are well-known and widely used mathematical formulations for modeling and analysis of signals in various applications. In this study, like the HT, to…
The embodied intelligence bridges the physical world and information space. As its typical physical embodiment, humanoid robots have shown great promise through robot learning algorithms in recent years. In this study, a hardware platform,…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
This paper presents an approach for the development of a number theoretic discrete Hilbert transform. The forward transformation has been applied by taking the odd reciprocals that occur in the DHT matrix with respect to a power of 2.…
The Delta-variance analysis, has proven to be an efficient and accurate method of characterising the power spectrum of interstellar turbulence. The implementation presently in use, however, has several shortcomings. We propose and test an…
Multi-scale Vision Transformer (ViT) has emerged as a powerful backbone for computer vision tasks, while the self-attention computation in Transformer scales quadratically w.r.t. the input patch number. Thus, existing solutions commonly…
We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel…
The Quantum Wheeler-DeWitt operator can be derived from an affine commutation relation via the affine group representation formalism for gravity, wherein a family of gauge-diffeomorphism invariant affine coherent states are constructed from…
The extensive adoption of web technologies in the finance and investment sectors has led to an explosion of financial data, which contributes to the complexity of the forecasting task. Traditional machine learning models exhibit limitations…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
Some conventional transforms such as Discrete Walsh-Hadamard Transform (DWHT) and Discrete Cosine Transform (DCT) have been widely used as feature extractors in image processing but rarely applied in neural networks. However, we found that…
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear…
The dual-fermion approach offers a way to perform diagrammatic expansion around the dynamical mean-field theory. Using this formalism, the influence of antiferromagnetic fluctuations on the self-energy is taken into account through…
Transient signals are often composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), which brings challenges to the development of signal processing technology. Fortunately, the group delay (GD) of…
We prove several universal properties of charge transport in generic CFTs holographic to nonminimal extensions of four-dimensional Einstein-Maxwell theory with exact electromagnetic duality invariance. First, we explicitly verify that the…
A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the…
Far-field Wireless Power Transfer (WPT) has attracted significant attention in the last decade. Recently, channel-adaptive waveforms have been shown to significantly increase the DC power level at the output of the rectifier. However the…