Related papers: The twist for electrical networks and the inverse …
We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman integrals. We propose a novel, more efficient algorithm to compute Macaulay…
A grove is a spanning forest of a planar graph in which every component tree contains at least one of a special subset of vertices on the outer face called nodes. For the natural probability measure on groves, we compute various connection…
We address the discrete inverse conductance problem for well-connected spider networks; that is, to recover the conductance function on a well-connected spider network from the Dirichlet-to-Neumann map. It is well-known that this inverse…
Canonical twistor fibrations lead to Pfaffian systems by means of their superhorizontal distribution. The aim of this note is to identify explicitly the Pfaffian systems of five or less variables that arise in this way in terms of the…
We determine the twist in a birefringent optical fiber from measurements, at one end of the fiber, of the fiber response to an impulsive source at the same end. This is the inverse problem of determining a non-constant coefficient, of a…
The electronic properties of graphene under any arbitrary uniaxial strain field are obtained by an exact mapping of the corresponding tight-binding Hamiltonian into an effective one-dimensional modulated chain. For a periodic modulation,…
Experiments on bilayer graphene unveiled a fascinating realization of stacking disorder where triangular domains with well-defined Bernal stacking are delimited by a hexagonal network of strain solitons. Here we show by means of numerical…
For inversion-symmetric topological insulators and superconductors characterized by ${\mathbb Z}_{2}$ topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling…
We study an inverse scattering problem for Maxwell's equations in terminating waveguides, where localized reflectors are to be imaged using a remote array of sensors. The array probes the waveguide with waves and measures the scattered…
We address the problem of identifying a graph structure from the observation of signals defined on its nodes. Fundamentally, the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable…
We present a symmetry analysis of the trigonal band structure in graphene, elucidating the transformational properties of the underlying basis functions and the crucial role of time-reversal invariance. Group theory is used to derive an…
It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the…
We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…
In a recent paper Jones introduced a correspondence between elements of the Thompson group $F$ and certain graphs/links. It follows from his work that several polynomial invariants of links, such as the Kauffman bracket, can be…
Cactus networks were introduced by Lam as a generalization of planar electrical networks. He defined a map from these networks to the Grassmannian Gr($n+1,2n$) and showed that the image of this map, $\mathcal X_n$ lies inside the totally…
We show how to recover a discrete twist over an ample Hausdorff groupoid from a pair consisting of an algebra and what we call a quasi-Cartan subalgebra. We identify precisely which twists arise in this way (namely, those that satisfy the…
We present a few ways of using conformal maps in the reconstruction of two-dimensional conductivities in electrical impedance tomography. First, by utilizing the Riemann mapping theorem, we can transform any simply connected domain of…
Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…
Given a graph and one of its weighted Laplacian matrix, a Fiedler vector is an eigenvector with respect to the second smallest eigenvalue. The Fiedler vectors have been used widely for graph partitioning, graph drawing, spectral clustering,…
We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…