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Recent advancements in Multimodal Large Language Models (MLLMs) have significantly enhanced performance on 2D visual tasks. However, improving their spatial intelligence remains a challenge. Existing 3D MLLMs always rely on additional 3D or…
Explicit algebraic expressions for the expansion of the vibrational matrix elements in series of matrix elements on the wave functions of the ground vibrational state have been obtained for arbitrary sufficiently differentiable functions of…
Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…
To date, various speech technology systems have adopted the vocoder approach, a method for synthesizing speech waveform that shows a major role in the performance of statistical parametric speech synthesis. WaveNet one of the best models…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Several large-scale gravitational wave (GW) interferometers have achieved long term operation at design sensitivity. Questions arise on how to best combine all available data from detectors of different sensitivities for detection,…
We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions…
We present a thorough study of the differential geometry of weightings and develop the theory of weightings for vector bundles, Lie groupoids, and Lie algebroids. We begin by extending the work of Loizides and Meinrenken on weighted…
A rigorous formulation of Vessiot's vector field approach to the analysis of general systems of partial differential equations is provided. It is shown that this approach is equivalent to the formal theory of differential equations and that…
Employing large antenna arrays is a key characteristic of millimeter wave (mmWave) and terahertz communication systems. However, due to the adoption of fully analog or hybrid analog/digital architectures, as well as non-ideal hardware or…
Multiview learning (MvL) is an advancing domain in machine learning, leveraging multiple data perspectives to enhance model performance through view-consistency and view-discrepancy. Despite numerous successful multiview-based SVM models,…
Adaptive mesh refinement techniques are nowadays an established and powerful tool for the numerical discretization of PDE's. In recent years, wavelet bases have been proposed as an alternative to these techniques. The main motivation for…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
An original multiplex scheme is introduced, which is based on Mallat's multiresolution formulation of wavelet systems. This system is adaptable and its implementation is well matched to digital signal processors and computers. The approach…
In this paper we present a general approach to multivariate periodic wavelets generated by scaling functions of de la Vall\'ee Poussin type. These scaling functions and their corresponding wavelets are determined by their Fourier…
Efficient ways to prepare fermionic ground states on quantum computers are in high demand and different techniques have been developed over the last years. Despite having a vast set of methods, it is still unclear which method performs well…
We introduce a general framework for the construction of polynomial frames in $L^2(\mathbb{S}^{d-1})$, $d \geq 3$, where the frame functions are obtained as rotated versions of an initial sequence of polynomials $\Psi^j$, $j\in…
We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L^2 function, a given likelihood function has an alternative representation as a product of…
A new way of constructing unextendible maximally entangled basis (UMEB) from maximally entangled basis (MEB) is proposed. Consequently, it is shown that if there is an $N$-member UMEB in $\mathbb{C}^d\otimes \mathbb{C}^d$, then there exists…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…