Related papers: The combinatorial geometry of stresses in framewor…
This paper addresses the problem of constructing bearing rigid networks in arbitrary dimensions. We first show that the bearing rigidity of a network is a generic property that is critically determined by the underlying graph of the…
We characterize the combinatorial types of symmetric frameworks in the plane that are minimally generically symmetry-forced infinitesimally rigid when the symmetry group consists of rotations and translations. Along the way, we use tropical…
In this paper we establish combinatorial characterisations of symmetry-generic infinitesimally rigid frameworks in the Euclidean plane for rotational groups of order 4 and 6, and of odd order between 5 and 1000, where a joint may lie at the…
The problem of finding the general classification of geodetic graphs is still open. We believe that one of the obstacles to attain this goal is that geodetic graphs lack a structural description. In other words, their fundamental properties…
The paper discusses the conditions for the existence of fixed points of multivalued mappings that are not based on the linear structure of the set. The descriptions for the sets of fixed points for mappings with closed graph in compact…
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…
Recent work has shown that if an isostatic bar and joint framework possesses non-trivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are `fixed' by various symmetry operations…
There are a variety of existing conditions for a degree sequence to be graphic. When a degree sequence satisfies any of these conditions, there exists a graph that realizes the sequence. We formulate several novel sufficient graphicality…
This paper presents a comprehensive analysis of junction conditions for gluing different $f(R)$ gravitational theories across a non-null hypersurface. Using the variational approach, we systematically derive the junction conditions for both…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
In 2005, Bob Connelly showed that a generic framework in $\bR^d$ is globally rigid if it has a stress matrix of maximum possible rank, and that this sufficient condition for generic global rigidity is preserved by the 1-extension operation.…
In this article we discuss a possibility to implement a well-known scheme of proof for contraction mapping theorems in a situation, when convergence, families of Cauchy sequences, and contractiveness of mappings are defined axiomatically.…
Generalized (rational) graph contractions in the framework of a dislocated metric space endowed with a directed graph are investigated. Fixed point results for set-contractions are obtained. We also provide some examples to illustrate our…
In this present article, we get sufficient conditions for the existence and uniqueness of fixed points and common fixed points for single and double mapping satisfying various contractive conditions within the partially ordered…
The junction conditions for general theories of gravity based on actions that depend on arbitrary functions of the curvature scalar invariants (including differential invariants) are obtained using the distributional formalism. In case of…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
Consider a random geometric graph over a random point process in $\mathbb{R}^d$. Two points are connected by an edge if and only if their distance is bounded by a prescribed distance parameter. We show that projecting the graph onto a two…
We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.
In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. Using this framework, it is…
The geometrical formulation of gravity is not unique and can be set up in a variety of spacetimes. Even though the gravitational sector enjoys this freedom of different geometrical interpretations, consistent matter couplings have to be…