Related papers: The construction of a completely scrambled system …
We analyse the solutions of networked heterogeneous nonlinear systems. We assume that the closed-loop interconnected systems form a network with an underlying connected directed graph that contains a directed spanning tree. For these…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
Self-folding is an emerging paradigm for the inverse design of three-dimensional structures. While most efforts have concentrated on the shape of the net, our approach introduces a new design dimension-bond specificity between the edges. We…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…
Twisted hypercubes are graphs that generalize the structure of the hypercube by relaxing the symmetry constraint while maintaining degree-regularity and connectivity. We study the zero forcing number of twisted hypercubes. Zero forcing is a…
The scramble number of a graph, a natural generalization of bramble number, is an invariant recently developed to study chip-firing games and graph gonality. We introduce the carton number of a graph, defined to be the minimum size of a…
The scramble number of a graph provides a lower bound for gonality and an upper bound for treewidth, making it a graph invariant of interest. In this paper we study graphs of scramble number at most two, and give a classification of all…
Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters…
In this paper, we extend the ideas of graph pebbling to oriented graphs and find a classification for all graphs with fully traversable pebbling assignments that are isomorphic to their assignment graph. We then give some cases in which a…
In the present paper, complete designs of graphs are considered. The notion of (regular) sampling is introduced and analyzed in detail, showing that the trivial necessary condition for its existence is actually sufficient. Some examples are…
We introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call "extender" and "hypershallow" graph sequences, respectively. Our main result is a probabilistic…
Two of the natural topologies for infinite graphs with edge-ends are Etop and Itop. In this paper, we study and characterize them. We show that Itop can be constructed by inverse limits of inverse systems of graphs with finitely many…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
A new method for constructing absolutely continuous two--dimensional copulas by differential equations is presented. The copulas are symmetric with respect to reflection in the opposite diagonal. The support of the copula density may be…
We consider a directed acyclic network with multiple sources and multiple terminals where each terminal is interested in decoding the sum of independent sources generated at the source nodes. We describe a procedure whereby a simple…
Every countable graph can be built from finite graphs by a suitable infinite process, either adding new vertices randomly or imposing some rules on the new edges. On the other hand, a profinite topological graph is built as the inverse…
We study some new dynamical systems where the corresponding piecewise linear flow is neither time reversible nor measure preserving. We create a dissipative system by starting with a finite polysquare translation surface, and then modifying…