Related papers: Directed and multi-directed animals on the king's …
In this paper, we introduce the notion of a finite non-simple directed graph, called an ornated graph and initiate a study on ornated graphs. An ornated graph is a directed graph on $n$ vertices, denoted by $O_n(s_l)$, whose vertices are…
We consider leader-follower multi-agent systems in which the leader executes the desired trajectory and the followers implement the consensus algorithm subject to stochastic disturbances. The performance of the leader-follower systems is…
Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment (UA) rules. When a new edge is created, with probability $p\in [0,1]$, it follows…
The learning efficiency and generalization ability of an intelligent agent can be greatly improved by utilizing a useful set of skills. However, the design of robot skills can often be intractable in real-world applications due to the…
A mathematical theory on flocking serves the foundation for several ubiquitous multi-agent phenomena in biology, ecology, sensor networks, economy, as well as social behavior like language emergence and evolution. Directly inspired by the…
Online social networks have emerged as useful tools to communicate or share information and news on a daily basis. One of the most popular networks is Twitter, where users connect to each other via directed follower relationships.…
A recurrence relation of the generating function of the dimer model of Fibonacci type gives a functional relation for formal power series associated to lattice paths such as a Dyck, Motzkin and Schr\"oder path. In this paper, we generalize…
We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges…
A class of countable infinite graphs with unbounded vertex degree is considered. In these graphs, the vertices of large degree `repel' each other, which means that the path distance between two such vertices cannot be smaller than a certain…
In this paper we introduce a novel family of decision lists consisting of highly interpretable models which can be learned efficiently in a greedy manner. The defining property is that all rules are oriented in the same direction.…
In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method of multipliers encounters troubles in both…
We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We…
Numerical reasoning over texts, such as addition, subtraction, sorting and counting, is a challenging machine reading comprehension task, since it requires both natural language understanding and arithmetic computation. To address this…
A king in a directed graph is a node from which each node in the graph can be reached via paths of length at most two. There is a broad literature on tournaments (completely oriented digraphs), and it has been known for more than half a…
Based on algebraic number theory we construct some families of rotated Dn-lattices with full diversity which can be good for signal transmission over both Gaussian and Rayleigh fading channels. Closed-form expressions for the minimum…
Probabilistic message-passing algorithms are developed for routing transmissions in multi-wavelength optical communication networks, under node and edge-disjoint routing constraints and for various objective functions. Global routing…
This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…
In the random case setting, scrambled polynomial lattice rules as discussed in \cite{BD10} enjoy more favourable strong tractablility properties than scrambled digital nets. This short note discusses the application of scrambled polynomial…