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Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
Irregular conformal block is an important tool to study a new type of conformal theories, which can be constructed as the colliding limit of the regular conformal block. The irregular conformal block is realized as the $\beta$-deformed…
The issue raised in this paper is classical in the sense of being ancient: which subset of 4X4 matrices should be accepted as physical Mueller matrices in polarization optics? Non-quantum entanglement between the polarization and spatial…
Polarised neutron scattering is the method of choice to study magnetism in condensed matter. Polarised neutrons are typically very low in flux, and complex experimental configurations further reduce the count rate. Neutron polarisation…
The longitudinal and transverse coupling impedances of a small discontinuity on the accelerator chamber wall can be expressed in terms of the electric and magnetic polarizabilities of the discontinuity. The polarizabilities are geometrical…
In-line polarimeters perform non-destructive polarization measurements of optical signals, and play a critical role in monitoring and controlling the polarization environment in for example optical networks. While current in-line…
Linear compartmental models are a widely used tool for analyzing systems arising in biology, medicine, and more. In such settings, it is essential to know whether model parameters can be recovered from experimental data. This is the…
Parameter identifiability is often requisite to the effective application of mathematical models in the interpretation of biological data, however theory applicable to the study of partial differential equations remains limited. We present…
We propose an imaging method to enhance and reveal structures within samples by using a polarization-based filter. This filter removes the isotropic content while amplifying the anisotropic component of depolarization. Whereas isotropic…
Medical image registration aims at identifying the spatial deformation between images of the same anatomical region and is fundamental to image-based diagnostics and therapy. To date, the majority of the deep learning-based registration…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
Spectroscopic ellipsometry (SE) has emerged as a powerful and non-destructive optical characterization technique for probing the complex dielectric properties of two-dimensional (2D) materials. This review provides a comprehensive overview…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
Materials with heterogeneous structures exhibit complex physical processes such as delamination, cracks, and plasticity, which require micromechanical parameters for understanding. However, identifying these parameters is challenging due to…
A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…
A single measurement of linear polarization of a nonthermal source provides direct information about the mean direction and level of ordering of the magnetic field. Monitoring of the polarization in blazars, combined with millimeter-wave…
In this article, we derive a Cauer network reluctivity model for soft magnetic composite materials. The Cauer network components are closed-form expressions consisting only of such parameters that have a clear physical meaning. The…
The polarization state of light is a key parameter in many imaging systems. For example, it can image mechanical stress and other physical properties that are not seen with conventional imaging, and can also play a central role in quantum…
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a…
We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform…