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Biinvariant means on Lie groups with CartanSchouten connections
, 2013
"... The statistical Riemannian framework was pretty well developped for finitedimensional manifolds [28, 20, 22, 6, 7, 8, 23]. For Lie groups, left or right invariant metric provide a nice setting as the Lie group becomes a geodesically complete Riemannian manifold, thus also metrically complete. Howeve ..."
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. However, this Riemannian approach is fully consistent with the group operations only if a biinvariant metric exists. Unfortunately, biinvariant Riemannian metrics do not exist on most non compact and noncommutative Lie groups. In particular, such metrics do not exist in any dimension for rigid
BIINVARIANT METRICS ON THE GROUP OF SYMPLECTOMORPHISMS
, 2005
"... Abstract. This paper studies the extension of the Hofer metric and general Finsler metrics on Hamiltonian symplectomorphism group Ham(M, ω) to the identity component Symp 0 (M, ω) of symplectomorphism group. In particular, we prove that the Hofer metric on Ham(M, ω) does not extend to a biinvariant ..."
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Cited by 5 (2 self)
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Abstract. This paper studies the extension of the Hofer metric and general Finsler metrics on Hamiltonian symplectomorphism group Ham(M, ω) to the identity component Symp 0 (M, ω) of symplectomorphism group. In particular, we prove that the Hofer metric on Ham(M, ω) does not extend to a biinvariant
Critical Power for Asymptotic Connectivity in Wireless Networks
, 1998
"... : In wireless data networks each transmitter's power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In particular, if the nodes in the network are assumed to cooperate in routing each others ' pack ..."
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Cited by 548 (19 self)
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; packets, as is the case in ad hoc wireless networks, each node should transmit with just enough power to guarantee connectivity in the network. Towards this end, we derive the critical power a node in the network needs to transmit in order to ensure that the network is connected with probability one
A Spatial Logic based on Regions and Connection
 PROCEEDINGS 3RD INTERNATIONAL CONFERENCE ON KNOWLEDGE REPRESENTATION AND REASONING
, 1992
"... We describe an interval logic for reasoning about space. The logic simplifies an earlier theory developed by Randell and Cohn, and that of Clarke upon which the former was based. The theory supports a simpler ontology, has fewer defined functions and relations, yet does not suffer in terms of its us ..."
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Cited by 736 (32 self)
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We describe an interval logic for reasoning about space. The logic simplifies an earlier theory developed by Randell and Cohn, and that of Clarke upon which the former was based. The theory supports a simpler ontology, has fewer defined functions and relations, yet does not suffer in terms of its useful expressiveness. An axiomatisation of the new theory and a comparison with the two original theories is given.
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules
, 2002
"... In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on ..."
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Cited by 1245 (60 self)
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In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its \neighbors." In their paper, Vicsek et. al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models.
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
Distributed hierarchical processing in the primate cerebral cortex
 Cereb Cortex
, 1991
"... In recent years, many new cortical areas have been identified in the macaque monkey. The number of identified connections between areas has increased even more dramatically. We report here on (1) a summary of the layout of cortical areas associated with vision and with other modalities, (2) a comput ..."
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Cited by 901 (6 self)
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In recent years, many new cortical areas have been identified in the macaque monkey. The number of identified connections between areas has increased even more dramatically. We report here on (1) a summary of the layout of cortical areas associated with vision and with other modalities, (2) a
Monetary Policy Shocks: What Have we Learned and to What End?
, 1998
"... This paper reviews recent research that grapples with the question: What happens after an exogenous shock to monetary policy? We argue that this question is interesting because it lies at the center of a particular approach to assessing the empirical plausibility of structural economic models that c ..."
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Cited by 967 (25 self)
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This paper reviews recent research that grapples with the question: What happens after an exogenous shock to monetary policy? We argue that this question is interesting because it lies at the center of a particular approach to assessing the empirical plausibility of structural economic models
Quantile Regression
 JOURNAL OF ECONOMIC PERSPECTIVES—VOLUME 15, NUMBER 4—FALL 2001—PAGES 143–156
, 2001
"... We say that a student scores at the fifth quantile of a standardized exam if he performs better than the proportion � of the reference group of students and worse than the proportion (1–�). Thus, half of students perform better than the median student and half perform worse. Similarly, the quartiles ..."
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Cited by 937 (10 self)
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of 166 firms, we compute the three quartiles of CEO compensation: salary, bonus and other compensation, including stock options (as valued by the BlackScholes formula at the time of the grant). For each group, the bowtielike box represents the middle half of the salary distribution lying between
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