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Cancer survival analysis commonly integrates information across diverse medical modalities to make survival-time predictions. Existing methods primarily focus on extracting different decoupled features of modalities and performing fusion…

The substantial computational costs of diffusion models, especially due to the repeated denoising steps necessary for high-quality image generation, present a major obstacle to their widespread adoption. While several studies have attempted…

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For…

In precision frequency transfer systems, stringent requirements are imposed on the phase stability of transmitted signals. Throughout the transmission process, the inherent challenges of long-haul signal propagation inevitably introduce…

In this paper we give an integral representation of an $n$-convex function $f$ in general case without additional assumptions on function $f$. We prove that any $n$-convex function can be represented as a sum of two $(n+1)$-times monotone…

It is often useful to perform integration over learned functions represented by neural networks. However, this integration is usually performed numerically, as analytical integration over learned functions (especially neural networks) is…

Deep Convolutional Neural Networks (CNNs) have been widely used in various domains due to their impressive capabilities. These models are typically composed of a large number of 2D convolutional (Conv2D) layers with numerous trainable…

Deriving an effective facial expression recognition component is important for a successful human-computer interaction system. Nonetheless, recognizing facial expression remains a challenging task. This paper describes a novel approach…

We show that the CFT with symmetry group $G_{k_1}\times G_{k_2}\times \cdots \times G_{k_n}$ consisting of WZW models based on the same group $G$, but at arbitrary integer levels, admits an integrable deformation depending on $2(n-1)$…

Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…

We consider the problem of demixing a sequence of source signals from the sum of noisy bilinear measurements. It is a generalized mathematical model for blind demixing with blind deconvolution, which is prevalent across the areas of…

The emergence of deep learning has stimulated a new class of PDE solvers in which the unknown solution is represented by a neural network. Within this framework, residual minimization in dual norms -- central to weak adversarial neural…

This paper presents some absorbing boundary conditions (ABC) for simulations based on the time-dependent density-functional theory (TDDFT). The boundary conditions are expressed in terms of the elements of the density-matrix, and it is…

The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…

An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…

Quantum-mechanical simulations can offer atomic-level insights into chemical processes on surfaces. This understanding is crucial for the rational design of new solid catalysts as well as materials to store energy and mitigate greenhouse…

Feature removal from computational geometries, or defeaturing, is an integral part of industrial simulation pipelines. Defeaturing simplifies the otherwise costly or even impossible meshing process, speeds up the simulation, and lowers its…

Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model…

We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…

Solving PDEs with machine learning techniques has become a popular alternative to conventional methods. In this context, Neural networks (NNs) are among the most commonly used machine learning tools, and in those models, the choice of an…