Related papers: Analytic equivalence of geometric transitions
This paper considers the topological degree of $G$-shifts of finite type for the case where $G$ is a nonabelian monoid. Whenever the Cayley graph of $G$ has a finite representation and the relationships among the generators of $G$ are…
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…
In this contribution, a mathematical framework is constructed to relate and compare non-linear partial differential equations (PDEs) in the category of smooth manifolds. In particular, it can be used to compare those aspects of field…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of…
This paper focuses on the problem of the degree sequence for a mixed random graph process which continuously combines the {\it classical} model and the BA model. Note that the number of step added edges for the mixed model is random and…
I extend the framework of rigid analytic geometry to the setting of algebraic geometry relative to monoids, and study the associated notions of separated, proper, and overconvergent morphisms. The category of affine manifolds embeds as a…
A geometric graph is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position. Two geometric realizations of a simple graph are geo-isomorphic if there is a vertex bijection between them…
This is one of a series of papers which aim towards a classification of edge-transitive maps of which the Euler characteristic and the edge number are coprime. This one establishes a framework and carries out the classification work for…
Lane-level traversal of (almost) arbitrary input paths is a common problem in the mapping industry. This paper considers the problem of generating \emph{feasible} and maximally convenient lane-level path traversals. The presented approach…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
This final degree project is devoted to study the topological classification of complex plane curves. These are subsets of $\mathbb{C}^2$ that can be described by an equation $f(x,y)=0$. Loosely speaking, curves are said to be equivalent in…
We define the \emph{occurrence graph} $G_p(\pi$) of a pattern $p$ in a permutation $\pi$ as the graph with the occurrences of $p$ in $\pi$ as vertices and edges between the vertices if the occurrences differ by exactly one element. We then…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…
Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important…
Given an indexed family ${\cal A} = (A_1, A_2, \dotsc, A_n)$ of subsets of some given set $S$, a \emph{transversal} is a set of distinct elements $x_1, x_2, \dotsc, x_n$ with each $x_i \in A_i$. Transversals have been studied since 1935 and…
Graph cut problems are fundamental in Combinatorial Optimization, and are a central object of study in both theory and practice. Furthermore, the study of \emph{fairness} in Algorithmic Design and Machine Learning has recently received…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…