Related papers: The twist for electrical networks and the inverse …
We study a new invariant of circular planar electrical networks, well known to phylogeneticists: the circular split system. We use our invariant to answer some open questions about levels of complexity of networks and their related…
A new way of computing scattering amplitudes in a certain very important QFT (N=4 SYM) has recently been developed, in which an algebraic structure called the positive Grassmannian plays a very important role. The mathematics of the…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) resistors. Generalizing work of Curtis, Ingerman, Morrow, Colin de Verdiere, Gitler, and Vertigan, we characterize…
We study the inverse eigenvector centrality problem on connected undirected graphs, namely, whether a given positive vector can be realized by assigning suitable edge weights. We provide a complete characterization in terms of stable sets…
Trace maps of two-letter substitution rules are investigated with special emphasis on the underlying algebraic structure and on the existence of invariants. We illustrate the results with the generalized Fibonacci chains and show that the…
Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance…
We consider the mapping of tight-binding electronic structure theory to a local spin Hamiltonian, based on the adiabatic approximation for spin degrees of freedom in itinerant-electron systems. Local spin Hamiltonians are introduced in…
Strain soliton networks strongly influence the structural and electronic properties of heterodeformed bilayer systems, yet their design remains challenging due to the high dimensionality of heterodeformation space and the absence of a…
The study and calculation of spectrum of networks can be used to describe networks structure and quantify analysis of networks performance. The fractal M\"{o}bius octagonal networks, denoted by $Q_n$, is derived from the inverse…
The response matrix of a resistor network is the linear map from the potential at the boundary vertices to the net current at the boundary vertices. For circular planar resistor networks, Curtis, Ingerman, and Morrow have given a necessary…
In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…
Twisted bilayer graphene gives rise to large moir\'{e} patterns that form a triangular network upon mechanical relaxation. If gating is included, each triangular region has gapped electronic Dirac points that behave as bulk topological…
The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…
We introduce a natural generalization of twisted maps, called \emph{warped maps}. While twisted maps play an important role in the study of Deligne--Mumford stacks, warped maps are better suited for studying Artin stacks. Heuristically,…
We present a linear response calculation for twisted bilayer graphene. The calculation is performed for both the continuum and tight-binding models, with the aim of assessing the validity of the former. All qualitatively important features…
We introduce a new numerical invariant for special, reduced, alternating diagrams of oriented knots and links, defined in terms of the Laplacian matrix of the associated Tait graph. For a special alternating diagram, the Laplacian encodes…
We provide a method for the generation of effective continuum Hamiltonians that goes beyond the well known k.p method in being equally effective in both high, and low (or no) symmetry situations. Our approach is based on a surprising exact…
In this paper, we study forward problem and inverse problem for the fractional magnetic Schrodinger equation with nonlinear electric potential. We first investigate the maximum principle for the linearized equation and apply it to show that…
We derive electronic structure models for weakly interacting bilayers such as graphene-graphene and graphene-hexagonal boron nitride, based on density functional theory calculations followed by Wannier transformation of electronic states.…