Information flow and cooperative control of vehicle formations

We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability

Use of implicit graph for recommending relevant videos: a simulated evaluation

In this paper, we propose a model for exploiting community based usage information for video retrieval. Implicit usage information from a pool of past users could be a valuable source to address the difficulties caused due to the semantic gap problem. We propose a graph-based implicit feedback model in which all the usage information can be represented. A number of recommendation algorithms were suggested and experimented. A simulated user evaluation is conducted on the TREC VID collection and the results are presented. Analyzing the results we found some common characteristics on the best performing algorithms, which could indicate the best way of exploiting this type of usage information

Active Learning for Undirected Graphical Model Selection

This paper studies graphical model selection, i.e., the problem of estimating a graph of statistical relationships among a collection of random variables. Conventional graphical model selection algorithms are passive, i.e., they require all the measurements to have been collected before processing begins. We propose an active learning algorithm that uses junction tree representations to adapt future measurements based on the information gathered from prior measurements. We prove that, under certain conditions, our active learning algorithm requires fewer scalar measurements than any passive algorithm to reliably estimate a graph. A range of numerical results validate our theory and demonstrates the benefits of active learning.Comment: AISTATS 201

Cooperative Games in Graph Structure

By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition that is a nonempty subset of the grand coalition of all players.It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game.For this result any information on the internal organization of the coalition is neglected.In this paper we generalize the concept of coalitional games and allow for organizational structure within coalitions.For a subset of players any arbitrarily given structural relation represented by a graph is allowed for.We then consider non-transferable utility games in which a possibly empty set of payoff vectors is assigned to any graph on every subset of players.Such a game will be called a cooperative game in graph structure or shortly graph game.A payoff vector lies in the core of the game if there is no graph on a group of players which can make all of its members better off.We define the balanced-core of a graph game as a refinement of the core.To do so, for each graph a power vector is determined that depends on the relative positions of the players within the graph.A collection of graphs will be called balanced if to any graph in the collection a positive weight can be assigned such that the weighted power vectors sum up to the vector of ones.A payoff vector lies in the balanced-core if it lies in the core and the payoff vector is an element of payoff sets of all graphs in some balanced collection of graphs.We prove that any balanced graph game has a nonempty balanced-core and therefore a nonempty core.We conclude by some examples showing the usefulness of the concepts of graph games and balanced-core.In particular these examples show a close relationship between solutions to noncooperative games and balanced-core elements of a well-defined graph game.This places the paper in the Nash research program, looking for a unifying theory in which each approach helps to justify and clarify the other.cooperative games;graphs

Lower bounds on data collection time in sensory networks

Data collection, i.e., the aggregation at the user location of information gathered by sensor nodes, is a fundamental function of sensory networks. Indeed, most sensor network applications rely on data collection capabilities, and consequently, an inefficient data collection process may adversely affect the performance of the network. In this paper, we study via simple discrete mathematical models, the time performance of the data collection and data distribution tasks in sensory networks. Specifically, we derive the minimum delay in collecting sensor data for networks of various topologies such as line, multiline, and tree and give corresponding optimal scheduling strategies. Furthermore, we bound the data collection time on general graph networks. Our analyses apply to networks equipped with directional or omnidirectional antennas and simple comparative results of the two systems are presented