Related papers: Two New Gestures on Peirce's Continuum and the Exi…
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These…
We prove properties of extremal graphs of girth 5 and order 20 <=v <= 32. In each case we identify the possible minimum and maximum degrees, and in some cases prove the existence of (non-trivial) embedded stars. These proofs allow for…
We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…
In this work, we introduce a novel evaluation framework for generative models of graphs, emphasizing the importance of model-generated graph overlap (Chanpuriya et al., 2021) to ensure both accuracy and edge-diversity. We delineate a…
One of Erdos's conjectures states that every triangle-free graph on $n$ vertices has an induced subgraph on $n/2$ vertices with at most $n^2/50$ edges. We report several partial results towards this conjecture. In particular, we establish…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations…
In La G\'eom\'etrie, Descartes proposed a balance between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In modern terms, that is a balance between analog and symbolic computation.…
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions…
In this article we obtain new expressions for the generating functions counting (non-singular) walks with small steps in the quarter plane. Those are given in terms of infinite series, while in the literature, the standard expressions use…
We derive an expression for the mutual gravitational force and torque of two bodies having arbitrary shapes and mass distributions, as an expansion in power series of their products of inertia and of the relative coordinates of their…
For the case of evidence ordered in a complete directed acyclic graph this paper presents a new algorithm with lower computational complexity for Dempster's rule than that of step-by-step application of Dempster's rule. In this problem,…
There is an elegant relation found by Fabricius-Bjerre [Math. Scand 40 (1977) 20--24] among the double tangent lines, crossings, inflections points, and cusps of a singular curve in the plane. We give a new generalization to singular curves…
Dexterous grasping is a fundamental yet challenging skill in robotic manipulation, requiring precise interaction between robotic hands and objects. In this paper, we present $\mathcal{D(R,O)}$ Grasp, a novel framework that models the…
We present a graph-theoretic model for dynamical systems $(X,\sigma)$ given by a surjective local homeomorphism $\sigma$ on a totally disconnected compact metrizable space $X$. In order to make the dynamics appear explicitly in the graph,…
A new metric for quantifying pairwise vertex connectivity in graphs is defined and an implementation presented. While general in nature, it features a combination of input features well-suited for social networks, including applicability to…