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We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through…

This work explores the behaviour of demagnetizing tensors for general ellipsoids under arbitrary rotations in homogeneous magnetic fields. The work is motivated by the concerns in magnetic resonance imaging safety and their practical…

Spectroscopic properties of molecules holds great importance for the description of the molecular response under the effect of an UV/Vis electromagnetic radiation. Computationally expensive ab initio (e.g. MultiConfigurational SCF, Coupled…

This paper uses clustering algorithms to introduce a shape framework for deformable objects. Until now, the shape detection of the deformable objects has faced several challenges: 1) unable to form a unified framework for multiple shapes;…

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of…

Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

We present Shape-Tailored Deep Neural Networks (ST-DNN). ST-DNN extend convolutional networks (CNN), which aggregate data from fixed shape (square) neighborhoods, to compute descriptors defined on arbitrarily shaped regions. This is natural…

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of…

In order to investigate correspondences between 3D shapes, many methods rely on a feature descriptor which is invariant under almost isometric transformations. An interesting class of models for such descriptors relies on partial…

We introduce a regularization loss based on kernel mean embeddings with rotation-invariant kernels on the hypersphere (also known as dot-product kernels) for self-supervised learning of image representations. Besides being fully competitive…

We develop a convolutional regularized least squares ($\texttt{CRLS}$) framework for reduced-order modeling of transonic flows with shocks. Conventional proper orthogonal decomposition (POD) based reduced models are attractive because of…

Complex systems manifest a small number of instabilities and bifurcations that are canonical in nature, resulting in universal pattern forming characteristics as a function of some parametric dependence. Such parametric instabilities are…

An ill-posed inverse problem of autoconvolution type is investigated. This inverse problem occurs in nonlinear optics in the context of ultrashort laser pulse characterization. The novelty of the mathematical model consists in a physically…

Identifying new disease-related patterns in medical imaging data with the help of machine learning enlarges the vocabulary of recognizable findings. This supports diagnostic and prognostic assessment. However, image appearance varies not…

Changes in the extent of local concavity along with changes in surface roughness of binding sites of proteins have long been considered as useful markers to identify functional sites of proteins. However, an algorithm that describes the…

The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data…

Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…

We present a mathematical model to decompose a longitudinal deformation into normal and abnormal components. The goal is to detect and extract subtle quivers from periodic motions in a video sequence. It has important applications in…

Regularization in convolutional neural networks (CNNs) is usually addressed with dropout layers. However, dropout is sometimes detrimental in the convolutional part of a CNN as it simply sets to zero a percentage of pixels in the feature…