Related papers: Improved upper and lower bound techniques for mono…
L (Logarithmic space) versus NL (Non-deterministic logarithmic space) is one of the great open problems in computational complexity theory. In the paper "Bounds on monotone switching networks for directed connectivity", we separated…
In this paper, we prove almost tight bounds on the size of sound monotone switching networks accepting permutations sets of directed trees. This roughly corresponds to proving almost tight bounds bounds on the monotone memory efficiency of…
We separate monotone analogues of L and NL by proving that any monotone switching network solving directed connectivity on $n$ vertices must have size at least $n^(\Omega(\lg(n)))$.
In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are…
We prove that the directed graph reachability problem (transitive closure) can be solved by monotone fan-in 2 boolean circuits of depth (1/2+o(1))(log n)^2, where n is the number of nodes. This improves the previous known upper bound…
In this technical note, we study the controllability of diffusively coupled networks from a graph theoretic perspective. We consider leader-follower networks, where the external control inputs are injected to only some of the agents, namely…
We derive a new upper bound on the algebraic connectivity of a regular graph using the Higman-Sims technique. Together with a new result on the connectivity of the neighbourhood graph of strongly regular graphs, our result gives a…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
We establish a new relationship between monotonicity and contractivity and use this connection to describe a new general class of weakly contractive reaction networks. The new class is characterized by the stoichiometry matrix of the…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
Adaptive (or co-evolutionary) network dynamics, i.e., when changes of the network/graph topology are coupled with changes in the node/vertex dynamics, can give rise to rich and complex dynamical behavior. Even though adaptivity can improve…
In this paper, we study the problem of constructing a network by observing ordered connectivity constraints, which we define herein. These ordered constraints are made to capture realistic properties of real-world problems that are not…
Harry Buhrman et al gave an Omega(sqrt n) lower bound for monotone graph properties in the adjacency matrix query model. Their proof is based on the polynomial method. However for some properties stronger lower bounds exist. We give an…
We propose some kinetic models of wealth exchange and investigate their behavior on directed networks though numerical simulations. We observe that network topology and directedness yields a variety of interesting features in these models.…
Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in $R^n$, with the admissible set indexed by the time parameter. The…
Controlling a complex network is of great importance in many applications. The network can be controlled by inputting external control signals through some selected nodes, which are called input nodes. Previous works found that the majority…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…