Related papers: Structure functions and minimal path sets
In this paper we continue a long line of work on representing the cut structure of graphs. We classify the types minimum vertex cuts, and the possible relationships between multiple minimum vertex cuts. As a consequence of these…
Structural stiffness plays an important role in engineering design. The analysis of stiffness requires precise experiments and computational models that can be difficult or time-consuming to procure. A novel relation between modal and…
Graph classification is a highly impactful task that plays a crucial role in a myriad of real-world applications such as molecular property prediction and protein function prediction.Aiming to handle the new classes with limited labeled…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
In this paper we give an explicit characterization of o-minimal structures with definable Skolem functions/definable choice. Such structures are, after naming finitely many elements from the prime model, a union of finitely many trivial…
Given a set of points in the plane, a covering path is a polygonal path that visits all the points. In this paper we consider covering paths of the vertices of an n x m grid. We show that the minimal number of segments of such a path is…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
The present paper is a short review of different path integral representations of the partition function of quantum spin systems. To begin with, I consider coherent states for SU(2) algebra. Different parameterizations of the coherent…
We construct a binary minimal subshift whose words of length n form a connected subset of the Hamming graph for each n.
The {\it profile} of a relational structure $R$ is the function $\phi_R$ which counts for every integer $n$ the number of its $n$-element substructures up to an isomorphism. Many counting functions are profiles. Interesting examples come…
Symbolic execution is a powerful verification tool for hardware designs, but suffers from the path explosion problem. We introduce a new approach, piecewise composition, which leverages the modular structure of hardware to transfer the work…
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
We establish new results concerning endomorphisms of a finite chain if the cardinality of the image of such endomorphism is no more than some fixed number k. The semiring of all such endomorphisms can be seen as a k - simplex whose vertices…
We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are…
One major challenge of neuroscience is finding interesting structures in a seemingly disorganized neural activity. Often these structures have computational implications that help to understand the functional role of a particular brain…
We give a formula which determines the minimal effective dimensions of path semigroups and truncated path semigroups over an uncountable field of characteristic zero.
A self-contained account of the theory of structure trees for edge cuts in networks is given. Applications include a generalisation of the Max-Flow Min-Cut Theorem to infinite networks and a short proof of a conjecture of Kropholler. This…
In this paper, structural properties of lower semi-frames in separable Hilbert spaces are explored with a focus on transformations under linear operators (may be unbounded). Also, the direct sum of lower semi-frames, providing necessary and…
We characterize the signature of piecewise continuously differentiable paths transformed by a polynomial map in terms of the signature of the original path. For this aim, we define recursively an algebra homomorphism between two shuffle…
Fractal structure of shortest paths depends strongly on interresidue interaction cutoff distance. The dimensionality of shortest paths is calculated as a function of interaction cutoff distance. Shortest paths are self similar with a…