相关论文: Optimized numerical inverse Laplace transformation
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
Vision transformers have recently made a breakthrough in computer vision showing excellent performance in terms of precision for numerous applications. However, their computational cost is very high compared to alternative approaches such…
Implicit Neural Representations (INRs) parameterize continuous signals via multilayer perceptrons (MLPs), enabling compact, resolution-independent modeling for tasks like image, audio, and 3D reconstruction. However, fitting high-resolution…
In this paper we investigate all-at-once versus reduced regularization of dynamic inverse problems on finite time intervals $(0,T)$. In doing so, we concentrate on iterative methods and nonlinear problems, since they have already been shown…
In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…
We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of…
Full waveform inversion (FWI) is crucial for reconstructing high-resolution subsurface models, but it is often hindered, considering the limited data, by its null space resulting in low-resolution models, and more importantly, by its…
Massive MIMO systems have the potential to significantly enhance spectral efficiency, yet their widespread integration is hindered by the high power consumption of the underlying computations. This paper explores the applicability and…
This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine…
The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the…
This paper introduces an optimal representation for a right-to-left parallel elliptic curve scalar point multiplication. The right-to-left approach is easier to parallelize than the conventional left-to-right approach. However, unlike the…
Motivated by the efficiency investigation of the Tranformer-based transform coding framework, namely SwinT-ChARM, we propose to enhance the latter, as first, with a more straightforward yet effective Tranformer-based channel-wise…
The accelerated failure time (AFT) model is widely used to analyze relationships between variables in the presence of censored observations. However, this model relies on some assumptions such as the error distribution, which can lead to…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically…
Nuclear lattice effective field theory (NLEFT) is an efficient \textit{ab initio} tool for solving nuclear many-body systems using the imaginary-time projection technique, where the preparation of trial states is essential for substantially…
Implicit neural representations have recently demonstrated promising potential in arbitrary-scale Super-Resolution (SR) of images. Most existing methods predict the pixel in the SR image based on the queried coordinate and ensemble nearby…
Feature Transformation is crucial for classic machine learning that aims to generate feature combinations to enhance the performance of downstream tasks from a data-centric perspective. Current methodologies, such as manual expert-driven…
Lattice-based cryptography (LBC) exploiting Learning with Errors (LWE) problems is a promising candidate for post-quantum cryptography. Number theoretic transform (NTT) is the latency- and energy- dominant process in the computation of LWE…
We present the Fast Newton Transform (FNT), an algorithm for performing $m$-variate Newton interpolation in downward closed polynomial spaces with time complexity $\mathcal{O}(|A|m\overline{n})$. Here, $A$ is a downward closed set of…