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The FRS-ESR facility at GSI provides unique conditions for precision measurements of large areas on the nuclear mass surface in a single experiment. Values for masses of 604 neutron-deficient nuclides (30<=Z<=92) were obtained with a…
The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the…
The National Synchrotron Light Source II (NSLS-II) uses highly stable electron beam to produce high-quality X-ray beams with high brightness and low-emittance synchrotron radiation. The traditional algorithm to stabilize the beam applies…
A unique sample independent 3D self calibration methodology is tested on a unique optical coherence tomography and multi-spectral scanning laser ophthalmoscope (OCT-SLO) hybrid system. Operators visual cognition is replaced by computer…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
Most ordinary differential equation (ODE) models used to describe biological or physical systems must be solved approximately using numerical methods. Perniciously, even those solvers which seem sufficiently accurate for the forward…
This paper investigates the non-zero-sum linear-quadratic stochastic Stackelberg differential games with affine constraints, which depend on both the follower's response and the leader's strategy. With the help of the stochastic Riccati…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
This work presents a Network-Optimised Spiking (NOS) delay-aware scheduler for 6G radio access. The scheme couples a bounded two-state kernel to a clique-feasible proportional-fair (PF) grant head: the excitability state acts as a…
Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
In this work, we explore the entanglement structure of two $N = Z$ nuclei, $^{20}$Ne and $^{22}$Na using single-orbital entanglement entropy within the No-Core Shell Model (NCSM) framework for two realistic interactions, INOY and N$^3$LO.…
We present a new Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in which it is possible to use convex optimization to perform stability analysis with little or no conservatism. The first result gives…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…
Large language models (LLM) have emerged as a powerful tool for AI, with the key ability of in-context learning (ICL), where they can perform well on unseen tasks based on a brief series of task examples without necessitating any…
Random Matrix Theory (RMT) is capable of making predictions for the spectral fluctuations of a physical system only after removing the influence of the level density by unfolding the spectra. When the level density is known, unfolding is…
The first generic self-stabilizing transformer for local problems in a constrained bandwidth model is introduced. This transformer can be applied to a wide class of locally checkable labeling (LCL) problems, converting a given fault free…
Principled nonparametric tests for regression curvature in $\mathbb{R}^{d}$ are often statistically and computationally challenging. This paper introduces the stratified incomplete local simplex (SILS) tests for joint concavity of…
Unambiguous measurements play an important role in quantum information, with applications ranging from quantum key distribution to quantum state reconstruction. Recently, such measurements have also been used in quantum algorithms based on…