Related papers: Irreducibility and Rigidity in Digital Images
Micromechanical constitutive parameters are important for many engineering materials, typically in microelectronic applications and material design. Their accurate identification poses a three-fold experimental challenge: (i) deformation of…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
Superposing multiple plane waves can generate helicity lattices in which the optical helicity varies regularly in space. Here we propose an inverse design method for constructing arbitrary helicity structures based on placing a digital…
This paper treats the problem of the merging of formations, where the underlying model of a formation is graphical. We first analyze the rigidity and persistence of meta-formations, which are formations obtained by connecting several rigid…
We study signatures of physical constraints on free rotations of rigid bodies. We show analytically that the physical or non-physical nature of the moments of inertia of a system can be detected by qualitative changes both in the Montgomery…
We create plots of algebraic integers in the complex plane, exploring the effect of sizing the integers according to various arithmetic invariants. We focus on Galois theoretic invariants, in particular creating plots which emphasize…
Satellite imaging has a central role in monitoring, detecting and estimating the intensity of key natural phenomena. One important feature of satellite images is the trade-off between spatial/spectral resolution and their revisiting time, a…
Image dehazing deals with the removal of undesired loss of visibility in outdoor images due to the presence of fog. Retinex is a color vision model mimicking the ability of the Human Visual System to robustly discount varying illuminations…
The role of electronic correlations in Condensed Matter is at the heart of various important systems, like magnetic materials, superconductors, topological materials, optical lattices, etc. Electronic correlations are those which change the…
Uniaxial strain is a powerful tuning parameter that can control symmetry and anisotropic electronic properties in iron-based superconductors. However, accurately characterizing anisotropic strain can be challenging and complex. Here, we…
In the last two decades, Interactive White Boards (IWBs) have been widely available as a pedagogic tool. The usability of these boards for teaching disciplines where complex drawings are needed, we consider debatable in multiple regards. In…
We develop a rigidity theory for bar-joint frameworks in Euclidean $d$-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class.…
A model of soft frictionless disks in two dimensions at zero temperature is simulated with a shearing dynamics to study various kinds of asymmetries in sheared systems. We examine both single particle properties, the spatial velocity…
Density functional theory is used to study colloidal hard-rod fluids near an individual right-angled wedge or edge as well as near a hard wall which is periodically patterned with rectangular barriers. The Zwanzig model, in which the…
The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this paper, we describe a certified reduction strategy to deal with digital images, but preserving their…
Agents affected by their own future states in a one-dimensional discrete dynamical system (1-DDS) can replicate two-dimensional images. It is shown that such replication requires a toroidal spacetime and three rules are needed to calculate…
In this note we give an overview of rigidity properties and Loewy lengths of tilting modules in the BGG category O associated to a reductive Lie algebra. These results are well-known by several specialists, but seem difficult to find in the…
In the context of the variational bi-complex, we re-explain that irreducible gauge systems define a particular example of a Lie algebroid. This is used to review some recent and not so recent results on gauge, global and asymptotic…
We introduce abstract net spaces on directed sets and prove their embedding and interpolation properties. Typical examples of interest are lattices of irreducible unitary representations of compact Lie groups and of class I representations…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…