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Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether…
Developing particle-in-cell (PIC) methods using finite element basis sets, and without auxiliary divergence cleaning methods, was a long standing problem until recently. It was shown that if consistent spatial basis functions are used, one…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
We consider the problem in Electrical Impedance Tomography (EIT) of identifying one or multiple inclusions in a background-conducting body $\Omega\subset\mathbb{R}^2$, from the knowledge of a finite number of electrostatic measurements…
By working out the Bethe sum rule, a boundary condition that takes the form of a linear equality is derived for the fine structure observed in ionization edges present in electron energy-loss spectra. This condition is subsequently used as…
A version of the configuration interaction method, which has been recently developed to deal with large number of valence electrons, has been used to calculate magnetic dipole and electric quadrupole hyperfine structure constants for a…
Electronic Structure Theory (EST) describes the behavior of electrons in matter and is used to predict material properties. Conventionally, this involves forming a Hamiltonian and solving the Schr\"odinger equation through discrete…
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…
Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking…
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…
A novel Einstein relation (fractional Einstein relation, FER) for the electric conduction in non-crystalline semiconductors is presented. FER and the generalized Einstein relation (GER) [Phys. Rev. E 8, 1296 (1998)] are compared to the…
One of the common obstacles for learning causal models from data is that high-order conditional independence (CI) relationships between random variables are difficult to estimate. Since CI tests with conditioning sets of low order can be…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
In this paper we investigate the problem of identifying conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We…
Floating edge bands (FEB) have been identified in systems such as obstructed atomic insulators and layered nonsymmorphic semimetals, attracting considerable interest recently. Here we demonstrate that FEB can arise in a simplified model…
This paper proposes a new variational model by integrating the Allen-Cahn term with a local binary fitting energy term for segmenting images with intensity inhomogeneity and noise. An inhomogeneous graph Laplacian initialization method…
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…
This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy…
Over several decades, electromechanical impedance (EMI) measurements have been employed as a basis for structural health monitoring and damage detection. Traditionally, Root-mean-squared-deviation (RMSD) and Cross-correlation (XCORR) based…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…