Related papers: Power diagrams and Morse Theory
We present an approach to Morse theory on symmetric products of surfaces using the notion of folded ribbon trees. We introduce an $A_\infty$-category with objects defined as $\kappa$-tuples of Morse functions, where the differential of the…
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
Main subject of the paper is a (strong) Morse function on a compact manifold with boundary. We construct a cellular structure and discuss its algebraic properties in this paper. Also we get an estimation on Arnold's question on a number of…
Towards building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a topological ring. This requires building the theory of…
We show that the non-Archimedean skeleton of the $d$-th symmetric power of a smooth projective algebraic curve $X$ is naturally isomorphic to the $d$-th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of…
As a topic of mathematics, "arrangements", systems of hyperplanes, circles, and general (regular) submanifolds, attract us strongly. We present a natural elementary study of arrangements of circles. It is also a kind of new studies. Our…
A new discrete distribution has been proposed as a discrete analogue of the two sided power distribution [Van Drop, J. R. and Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation, Journal of the…
On a smooth manifold, we associate to any closed differential form a mapping cone complex. The cohomology of this mapping cone complex can vary with the de Rham cohomology class of the closed form. We present a novel Morse theoretical…
We show that an appropriate generalization of the oriented area function is a perfect Morse function on the space of three-dimensional configurations of an equilateral polygonal linkage with odd number of edges. Therefore cyclic equilateral…
In this paper we develop a Morse theory for the uniform energy. We use the one-sided directional derivative of the distance function to study the minimizing properties of variations through closed geodesics. This derivative is then used to…
We consider a differential geometric setting on power sets and Borel algebras. Our chosen framework is based on diffeologies, and we make a link between the various diffeological structures that we propose, having in mind set-valued maps,…
We investigate power series that converge to a bounded function on the real line. First, we establish relations between coefficients of a power series and boundedness of the resulting function; in particular, we show that boundedness can be…
We study how powerful algebraic discrete Morse theory is when applied to hull resolutions. The main result describes all cases when the hull resolution of the edge ideal of the complement of a triangle-free graph can be made minimal using…
The Stolz--Teichner program proposes a deep connection between geometric field theories and certain cohomology theories. In this paper, we extend this connection by developing a theory of geometric power operations for geometric field…
Based on our derivation of finite temperature reduced density matrix functional theory and the discussion of the performance of its first-order functional this work presents several different correlation-energy functionals and applies them…
Cohesive powers of computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let $\omega$, $\zeta$, and $\eta$ denote the respective order-types of the natural numbers, the integers, and…
Slicing a Voronoi tessellation in $\mathbb{R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the…
We comment on a recent paper that connects certain forms of machine learning to Set Theory. We point out that part of the set-theoretic machinery is related to a result of Kuratowski about decompositions of finite powers of sets and we show…
We study the holomorphic extension associated with power series, i.e., the analytic continuation from the unit disk to the cut-plane $\mathbb{C} \setminus [1,+\infty)$. Analogous results are obtained also in the study of trigonometric…