In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Ex Input:
Rough set theory, a mathematical tool to deal with vague concepts, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to covers. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the covers themselves, we introduce unary and composition operations on covers. A notion of homomorphism is provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.

Ex Output:
Covering rough sets based on neighborhoods


Ex Input:
In many applications spanning from sensor to social networks, transportation systems, gene regulatory networks or big data, the signals of interest are defined over the vertices of a graph. The aim of this paper is to propose a least mean square (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment.

Ex Output:
Least Mean Squares Estimation of Graph Signals


Ex Input:
There is an increasing need for automated support for humans monitoring the activity of distributed teams of cooperating agents, both human and machine. We characterize the domainindependent challenges posed by this problem, and describe how properties of domains influence the challenges and their solutions. We will concentrate on dynamic, data-rich domains where humans are ultimately responsible for team behavior. Thus, the automated aid should interactively support effective and timely decision making by the human. We present a domain-independent categorization of the types of alerts a plan-based monitoring system might issue to a user, where each type generally requires different monitoring techniques. We describe a monitoring framework for integrating many domain-specific and task-specific monitoring techniques and then using the concept of value of an alert to avoid operator overload. We use this framework to describe an execution monitoring approach we have used to implement Execution Assistants (EAs) in two different dynamic, data-rich, real-world domains to assist a human in monitoring team behavior. One domain (Army small unit operations) has hundreds of mobile, geographically distributed agents, a combination of humans, robots, and vehicles. The other domain (teams of unmanned ground and air vehicles) has a handful of cooperating robots. Both domains involve unpredictable adversaries in the vicinity. Our approach customizes monitoring behavior for each specific task, plan, and situation, as well as for user preferences. Our EAs alert the human controller when reported events threaten plan execution or physically threaten team members. Alerts were generated in a timely manner without inundating the user with too many alerts (less than 10% of alerts are unwanted, as judged by domain experts).

Ex Output:

Interactive Execution Monitoring of Agent Teams