Related papers: On Base Field of Linear Network Coding
The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…
Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…
Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…
Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…
In Francis and Steel (2015), it was shown that there exists non-trivial networks on $4$ leaves upon which the distance metric affords a metric on a tree which is not the base tree of the network. In this paper we extend this result in two…
In this paper, we study networks of discrete-time linear time-invariant subsystems. Our focus is on situations where subsystems are connected to each other through a time-invariant topology and where there exists a base-station whose aim is…
We give a closed formula for the dimension of all linear systems in $\mathbb{P}^n$ with assigned multiplicity at arbitrary collections of points lying on a rational normal curve of degree $n$. In particular we give a purely geometric…
In this paper, we provide some conditions of (super)-solvability and nilpotency of a finite group $G$ based on its number of subgroups $Sub(G)$. Our results generalize the classification of finite groups with less than $20$ subgroups by…
We study the sum capacity of multiple unicasts in wired and wireless multihop networks. With 2 source nodes and 2 sink nodes, there are a total of 4 independent unicast sessions (messages), one from each source to each sink node (this…
The resiliency of a network is its ability to remain \emph{effectively} functioning also when any of its nodes or links fails. However, to reduce operational and set-up costs, a network should be small in size, and this conflicts with the…
The optimization of multilayer neural networks typically leads to a solution with zero training error, yet the landscape can exhibit spurious local minima and the minima can be disconnected. In this paper, we shed light on this phenomenon:…
The multicut problem is an NP-hard combinatorial optimization problem with diverse applications in fields such as bioinformatics, data mining and computer vision. Graph neural networks have been defined for the multicut problem but can be…
The method for analyzing algorithmic runtime complexity using decision trees is discussed using the sorting algorithm. This method is then extended to optimal algorithms which may find all cliques of size q in network N, or simply the first…
We study the effect of limiting the number of different messages a node can transmit simultaneously on the verification complexity of proof-labeling schemes (PLS). In a PLS, each node is given a label, and the goal is to verify, by…
Insufficiency of linear coding for the network coding problem was first proved by providing an instance which is solvable only by nonlinear network coding (Dougherty et al., 2005).Based on the work of Effros, et al., 2015, this specific…
Fiber network modeling can be used for studying mechanical properties of paper. The individual fibers and the bonds in-between constitute a detailed representation of the material. However, detailed microscale fiber network models must be…
Emerging ad hoc networks are infrastructure-less networks consisting of wireless devices with various power constraints, capabilities and mobility characteristics. An essential capability in future ad hoc networks is the ability to provide…
Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of…
In this paper, we study distributed graph algorithms in networks in which the nodes have a limited communication capacity. Many distributed systems are built on top of an underlying networking infrastructure, for example by using a virtual…
This paper presents a first-order {distributed continuous-time algorithm} for computing the least-squares solution to a linear equation over networks. Given the uniqueness of the solution, with nonintegrable and diminishing step size,…