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Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichm\"uller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal…
We provide a further analysis of the class of positive maps proposed ten years ago by Kossakowski. In particular we propose a new parametrization which reveals an elegant geometric structure and an interesting interplay between group theory…
The conformal field theory on a Z_N-surface is studied by mapping it on the branched sphere. Using a coulomb gas formalism we construct the minimal models of the theory.
We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor of optimal in…
We consider several ways to test for topology directly in harmonic space by comparing the measured a_lm with the expected correlation matrices. Two tests are of a frequentist nature while we compute the Bayesian evidence as the third test.…
Conformal inference provides a rigorous statistical framework for uncertainty quantification in machine learning, enabling well-calibrated prediction sets with precise coverage guarantees for any classification model. However, its reliance…
We study the interplay between embedding constrained planarity and hybrid planarity testing. We consider a constrained planarity testing problem, called 1-Fixed Constrained Planarity, and prove that this problem can be solved in quadratic…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains on surfaces. In this paper the conjugate function method, earlier used for simply connected domains, is…
We extend a recent analysis of the pion electromagnetic form factor constrained by the conformal symmetry to explore the time-like region. We show explicitly that the time-like form factor obtained by the analytic continuation of the…
Planarity Testing is the problem of determining whether a given graph is planar while planar embedding is the corresponding construction problem. The bounded space complexity of these problems has been determined to be exactly Logspace by…
We investigate the proximal map for the weighted mean absolute error function. An algorithm for its efficient and vectorized evaluation is presented. As a demonstration, this algorithm is applied as part of a checkerboard algorithm to solve…
The Casimir effect in graphene systems is reviewed with emphasis made on the large thermal correction to the Casimir force predicted at short separations between the test bodies. The computational results for the Casimir pressure and for…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
A study prototype of Proximity Focussing Ring Imaging Cherenkov counter has been built and tested with several radiators using separately cosmic-ray particles and 12C beam fragmentation products at several energies. Counter prototype and…
We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a…
In this paper we consider the application of electromagnetic theory to the analysis of the Scanning Near-field Optical Microscope (SNOM) in order to predict experimentally observable quantities such as the transmission or reflection…
We determine both the magnetic potential and the electric potential from the exterior partial measurements of the Dirichlet-to-Neumann map in the fractional linear magnetic Calder\'on problem by using an integral identity. We also determine…
This note examines sufficient conditions for the quasiconformal extendibility of harmonic mappings defined in the unit disk. It is demonstrated that a harmonic strongly starlike mapping admits a quasiconformal extension to the entire plane,…
We carry out the homogenization of time-harmonic Maxwell's equations in a periodic, layered structure made of two-dimensional (2D) metallic sheets immersed in a heterogeneous and in principle anisotropic dielectric medium. In this setting,…
Transmission electron microscopy has been a promising candidate for mapping atomic orbitals for a long time. Here, we explore its capabilities by a first principles approach. For the example of defected graphene, exhibiting either an…