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In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
Surface-based data is commonly observed in diverse practical applications spanning various fields. In this paper, we introduce a novel nonparametric method to discover the underlying signals from data distributed on complex surface-based…
Accurate cardiac ultrasound segmentation is essential for reliable assessment of ventricular function in intelligent healthcare systems. However, echocardiographic images are challenging due to low contrast, speckle noise, irregular…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
Accurate lesion segmentation is crucial for clinical diagnosis and treatment planning. However, lesions often resemble surrounding tissues and exhibit ill-defined boundaries, leading to unstable predictions in boundary/transition regions.…
Topographic convolutional neural networks (TCNNs) are computational models that can simulate aspects of the brain's spatial and functional organization. However, it is unclear whether and how different types of topographic regularization…
The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles $\theta_1, \dots, \theta_n\in[0, 2\pi)$ from $m$ noisy measurements of their offsets $\theta_i-\theta_j \;\mbox{mod}…
In this article, we study a two-dimensional singularly perturbed parabolic equation of the convection-diffusion type, characterized by discontinuities in the source term and convection coefficient at a specific point in the domain. These…
Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an anomalous suppression of long-wavelength volume-fraction fluctuations, endowing them with novel physical properties. While such unusual…
One-class anomaly detection aims to detect objects that do not belong to a predefined normal class. In practice training data lack those anomalous samples; hence state-of-the-art methods are trained to discriminate between normal and…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…
This article studies the denoising performance of total variation (TV) image regularization. More precisely, we study geometrical properties of the solution to the so-called Rudin-Osher-Fatemi total variation denoising method. The first…
Unsupervised Graph Domain Adaptation (UGDA) seeks to bridge distribution shifts between domains by transferring knowledge from labeled source graphs to given unlabeled target graphs. Existing UGDA methods primarily focus on aligning…
Network or physical attacks on industrial equipment or computer systems may cause massive losses. Therefore, a quick and accurate anomaly detection (AD) based on monitoring data, especially the multivariate time-series (MTS) data, is of…
In radar systems, tracking targets in low signal-to-noise ratio (SNR) environments is a very important task. There are some algorithms designed for multitarget tracking. Their performances, however, are not satisfactory in low SNR…
Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and…
Recently, several instances of non-Euclidean SGD, including SignSGD, Lion, and Muon, have attracted significant interest from the optimization community due to their practical success in training deep neural networks. Consequently, a number…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…