Related papers: Statistical Topological Gradient and Shape Optimiz…
Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap,…
A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…
The surface code is a promising platform for a quantum memory, but its threshold under coherent errors remains incompletely understood. We study maximum-likelihood decoding of the square-lattice surface code in the presence of single-qubit…
This paper demonstrates the impact of a phase field method on shape registration to align shapes of possibly different topology. It yields new insights into the building of discrepancy measures between shapes regardless of topology, which…
In this work, we present a geometrical reconstruction of the critical points of the spinfoam amplitude for a 4D Lorentzian model with a non-zero cosmological constant. By establishing the correspondence between the moduli space of ${\rm…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
We develop a general framework unifying several gradient-based stochastic optimization methods for empirical risk minimization problems both in centralized and distributed scenarios. The framework hinges on the introduction of an augmented…
Topology optimization has emerged as a powerful and increasingly relevant strategy for enhancing the flexibility and efficiency of power system operations. However, solving these problems is computationally demanding due to their…
This paper establishes error bounds for the convergence of a piecewise linear approximation of the constrained optimal smoothing problem posed in a reproducing kernel Hilbert space (RKHS). This problem can be reformulated as a Bayesian…
Reconstructive spectrometers are a promising emerging class of devices that combine complex light scattering with inference to enable compact, high-resolution spectrometry. Thus far, the physical determinants of these devices' performance…
We analyze inexact Riemannian gradient descent (RGD) where Riemannian gradients and retractions are inexactly (and cheaply) computed. Our focus is on understanding when inexact RGD converges and what is the complexity in the general…
The aim of this article is to elaborate and rigorously analyze a topological derivative based imaging framework for locating an electromagnetic inclusion of diminishing size from boundary measurements of the tangential component of…
Leveraging our structure-adaptive topology optimization framework based on the integration of the photonic density of states over a frequency window for the TM polarization of light [see A. Bahulikar et al., arXiv:2411.09165 (2025)], we…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a domain $M \subset \R^n$ from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction formula…
Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…
This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. Boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional…
In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
We derive a vector generalization of the curvature-corrected Cram\'er--Rao bound (CRB) in the nonasymptotic regime using a Hilbert space square-root embedding. Building on previous scalar results, we establish a \emph{directional} curvature…