Related papers: Power diagrams and Morse Theory
We formulate the axioms of an orbifold theory with power operations. We define orbifold Tate K-theory, by adjusting Devoto's definition of the equivariant theory, and proceed to construct its power operations. We calculate the resulting…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}'…
Recent work on complex networks compared the topological and electrical structures of the power grid, taking into account the underlying physical laws that govern the electrical connectivity between various components in the network. A…
We study perturbation theory for spin foam models on triangulated manifolds. Starting with any model of this sort, we consider an arbitrary perturbation of the vertex amplitudes, and write the evolution operators of the perturbed model as…
Fermat-Weber points with respect to an asymmetric tropical distance function are studied. It turns out that they correspond to the optimal solutions of a transportation problem. The results are applied to obtain a new method for computing…
In this paper we present with algebraic trees a novel notion of (continuum) trees which generalizes countable graph-theoretic trees to (potentially) uncountable structures. For that purpose we focus on the tree structure given by the branch…
The distributions of the random distances associated with hexagons, rhombuses and triangles have been derived and verified in the existing work. All of these geometric shapes are related to each other and have various applications in…
We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in proximity of a superconductor. Using both analytical and numerical…
Fold maps are smooth maps at each singular point of which it is represented as the product map of a Morse function and the identity map. Round fold maps are, in short, such maps the sets of all singular points of which are embedded…
We develop Morse theory for manifolds with boundary. Besides standard and expected facts like the handle cancellation theorem and the Morse lemma for manifolds with boundary, we prove that, under a topological assumption, a critical point…
Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a complex $C$, from which topological and geometrical informations…
Subject of this paper is the theoretical analysis of structure-adaptive median filter algorithms that approximate curvature-based PDEs for image filtering and segmentation. These so-called morphological amoeba filters are based on a concept…
We conduct a study based on the Bures (minimal monotone) metric, analogous to that recently reported for the Hilbert-Schmidt (flat or Euclidean) metric (arXiv:0704.3723v2). Among the interesting results obtained there had been…
The problem of membrane topology in the matrix model of M-theory is considered. The matrix regularization procedure, which makes a correspondence between finite-sized matrices and functions defined on a two-dimensional base space, is…
In studies of smooth maps with good differential topological conditions such as immersions, embeddings, Morse functions and their higher dimensional versions including fold maps and application to geometry, especially algebraic and…
The Rooted Maps Theory, a branch of the Theory of Homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The…
In the setting of relative topos theory, we show that the pullback of a relative presheaf topos on an arbitrary fibration is the relative presheaf topos on its inverse image. To this end, we develop and exploit a notion of extension with…
We develop a discrete Morse theory for open simplicial complexes $K=X\setminus T$ where $X$ is a simplicial complex and $T$ a subcomplex of $X$. A discrete Morse function $f$ on $K$ gives rise to a discrete Morse function on the order…
We study the poset of Borel congruence classes of symmetric matrices ordered by containment of closures. We give a combinatorial description of this poset and calculate its rank function. We discuss the relation between this poset and the…
A wiring diagram is a labeled directed graph that represents an abstract concept such as a temporal process. In this article, we introduce the notion of a quasi-skeleton wiring diagram graph, and prove that quasi-skeleton wiring diagram…