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We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…
A novel general formalism for the maximal symetrization and reduction of fields (MSRF) is proposed and applied to wavefunctions in solid state nanostructures. Its primary target is to provide an essential tool for the study and analysis of…
Modern low-field magnetic resonance imaging (MRI) technology offers a compelling alternative to standard high-field MRI, with portable, low-cost systems. However, its clinical utility is limited by a low Signal-to-Noise Ratio (SNR), which…
Let $X$ be an unbounded metric space, $B(x,r) = \{y\in X: d(x,y) \leqslant r\}$ for all $x\in X$ and $r\geqslant 0$. We endow $X$ with the discrete topology and identify the Stone-\v{C}ech compactification $\beta X$ of $X$ with the set of…
In fetal Magnetic Resonance Imaging, Super Resolution Reconstruction (SRR) algorithms are becoming popular tools to obtain high-resolution 3D volume reconstructions from low-resolution stacks of 2D slices, acquired at different…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
Multi-slice magnetic resonance images of the fetal brain are usually contaminated by severe and arbitrary fetal and maternal motion. Hence, stable and robust motion correction is necessary to reconstruct high-resolution 3D fetal brain…
The problem of consistency of smoothed particle hydrodynamics (SPH) has demanded considerable attention in the past few years due to the ever increasing number of applications of the method in many areas of science and engineering. A loss…
Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…
In this paper, we provide a notion of $\infty$-bicategories fibred in $\infty$-bicategories which we call 2-Cartesian fibrations. Our definition is formulated using the language of marked biscaled simplicial sets: Those are scaled…
A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace $E$ of a dynamical system linearized at a fixed point. Passing from the full nonlinear dynamics to the flow on an…
Accurate nerve localization is critical for the success of ultrasound-guided regional anesthesia, yet manual identification remains challenging due to low image contrast, speckle noise, and inter-patient anatomical variability. This study…
Gravitational-wave parameter estimation for binary neutron star (BNS) systems poses severe computational challenges due to the extended signal duration, which can reach several minutes in current detectors. Neural posterior estimation…
On a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is invariant under the action of the diffeomorphism group, is a multiple of the Fisher--Rao…
Consider a class $\mH$ of binary functions $h: X\to\{-1, +1\}$ on a finite interval $X=[0, B]\subset \Real$. Define the {\em sample width} of $h$ on a finite subset (a sample) $S\subset X$ as $\w_S(h) \equiv \min_{x\in S} |\w_h(x)|$, where…
This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from Micro-CT images featuring intricate microstructures. The proposed method is guided by…
We present a rotation-equivariant unsupervised learning framework for the sparse deconvolution of non-negative scalar fields defined on the unit sphere. Spherical signals with multiple peaks naturally arise in Diffusion MRI (dMRI), where…
Scanning transmission X-ray microscopy and ptychography have become mature tools for high-resolution, element-specific imaging of nanoscale structures. However, transmission geometries impose stringent constraints on sample thickness and…
For any topological bicategory B, the Duskin nerve NB of B is a simplicial space. We introduce the classifying topos BB of B as the Deligne topos of sheaves Sh(NB) on the simplicial space NB. It is shown that the category of geometric…
We revisit the widely used bss eval metrics for source separation with an eye out for performance. We propose a fast algorithm fixing shortcomings of publicly available implementations. First, we show that the metrics are fully specified by…