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The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by…
We introuduce a unified method which can be applied to any WZW model at arbitrary level to search systematically for modular invariant physical partition functions. Our method is based essentially on modding out a known theory on group…
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces $L^2(\mu)$ with measures $\mu$ arising from iterated function systems (IFS). This includes equilibrium measures in complex dynamics.…
A novel approach to electronic correlations and magnetism of crystals based on realistic electronic structure calculations is reviewed. In its simplest form it is a combination of the ``local density approximation'' (LDA) and the dynamical…
We derive the multifractal analysis of the conformal measure (or equivalently, the invariant measure) associated to a family of weights imposed upon a (multi-dimensional) graph directed Markov system (GDMS) using balls as the filtration.…
We present a new on-shell method for the matching of ultraviolet models featuring massive states onto their massless effective field theory. We employ a dispersion relation in the space of complex momentum dilations to capture, in a single…
Recent studies provide evidence for the multi-scale nature of magnetic turbulence in the plasma sheet. Wavelet methods represent modern time series analysis techniques suitable for the description of statistical characteristics of…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
The derivative discontinuity in the exact exchange-correlation potential of ensemble Density Functional Theory (DFT) is investigated at the specific integer number that corresponds to the maximum number of bound electrons, $J_{max}$. A…
In this paper, an advanced fracture detection framework, FracDetNet, is proposed to address challenges in medical imaging, as accurate fracture detection is essential for enhancing diagnostic efficiency in clinical practice. Despite recent…
The detrended fluctuation analysis (DFA) [Peng et al., 1994] and its extensions (MF-DFA) [Kantelhardt et al., 2002] have been used extensively to determine possible long-range correlations in self-affine signals. While the DFA has been…
The increasing availability of sensor data at machine tools makes automatic chatter detection algorithms a trending topic in metal cutting. Two prominent and advanced methods for feature extraction via signal decomposition are Wavelet…
Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the…
Dual energy computed tomography (DECT) imaging plays an important role in advanced imaging applications due to its material decomposition capability. Image-domain decomposition operates directly on CT images using linear matrix inversion,…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
A new version of the invariant imbedding theory for the propagation of coupled waves in inhomogeneous media is applied to the mode conversion of high frequency electromagnetic waves into electrostatic modes in cold, magnetized and…
Accurate forecasting in financial markets requires integrating diverse data sources, from historical prices to macroeconomic indicators and financial news. However, existing models often fail to align these modalities effectively, limiting…
While Large Multimodal Models (LMMs) excel in general multimodal tasks, they lack the domain-specific knowledge for industrial vibration signal analysis. This paper introduces VSLLaVA, a comprehensive pipeline that utilizes expert…
It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…