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unknown title
, 2006
"... On the stability of periodic billiard paths in triangles A Dissertation, Presented by ..."
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On the stability of periodic billiard paths in triangles A Dissertation, Presented by
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1277 (120 self)
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edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two
Resilient Overlay Networks
, 2001
"... A Resilient Overlay Network (RON) is an architecture that allows distributed Internet applications to detect and recover from path outages and periods of degraded performance within several seconds, improving over today’s widearea routing protocols that take at least several minutes to recover. A R ..."
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Cited by 1160 (31 self)
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A Resilient Overlay Network (RON) is an architecture that allows distributed Internet applications to detect and recover from path outages and periods of degraded performance within several seconds, improving over today’s widearea routing protocols that take at least several minutes to recover. A
EndtoEnd Routing Behavior in the Internet
, 1996
"... The largescale behavior of routing in the Internet has gone virtually without any formal study, the exception being Chinoy's analysis of the dynamics of Internet routing information [Ch93]. We report on an analysis of 40,000 endtoend route measurements conducted using repeated “traceroutes” ..."
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Cited by 655 (13 self)
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, ” the likelihood that a route remains unchanged over a long period of time. We find that Internet paths are heavily dominated by a single prevalent route, but that the time periods over which routes persist show wide variation, ranging from seconds up to days. About 2/3's of the Internet paths had routes
EndtoEnd Internet Packet Dynamics,”
 Proc. SIGCOMM '97,
, 1997
"... Abstract We discuss findings from a largescale study of Internet packet dynamics conducted by tracing 20,000 TCP bulk transfers between 35 Internet sites. Because we traced each 100 Kbyte transfer at both the sender and the receiver, the measurements allow us to distinguish between the endtoend ..."
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Cited by 843 (19 self)
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toend behaviors due to the different directions of the Internet paths, which often exhibit asymmetries. We characterize the prevalence of unusual network events such as outoforder delivery and packet corruption; discuss a robust receiverbased algorithm for estimating "bottleneck bandwidth
Billiards in Nearly Isosceles Triangles
, 807
"... We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some selfsimilarity phenomena in irrational triangu ..."
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Cited by 5 (1 self)
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We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some selfsimilarity phenomena in irrational
Endtoend available bandwidth: Measurement methodology, dynamics, and relation with TCP throughput
 In Proceedings of ACM SIGCOMM
, 2002
"... The available bandwidth (availbw) in a network path is of major importance in congestion control, streaming applications, QoS verification, server selection, and overlay networks. We describe an endtoend methodology, called SelfLoading Periodic Streams (SLoPS), for measuring availbw. The basic ..."
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Cited by 414 (20 self)
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The available bandwidth (availbw) in a network path is of major importance in congestion control, streaming applications, QoS verification, server selection, and overlay networks. We describe an endtoend methodology, called SelfLoading Periodic Streams (SLoPS), for measuring availbw. The basic
Obtuse Triangular Billiards II: 100 Degrees Worth of Periodic Trajectories
"... We give a rigorous computerassisted proof that a triangle has a periodic billiard path provided all its angles are at most 100 degrees. One appealing thing about our proof is that the reader can use our software online to see massive visual evidence for our result and also to survey the computer pa ..."
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Cited by 9 (1 self)
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We give a rigorous computerassisted proof that a triangle has a periodic billiard path provided all its angles are at most 100 degrees. One appealing thing about our proof is that the reader can use our software online to see massive visual evidence for our result and also to survey the computer
Delayed internet routing convergence
 ACM SIGCOMM Computer Communication Review
, 2000
"... Abstract—This paper examines the latency in Internet path failure, failover, and repair due to the convergence properties of interdomain routing. Unlike circuitswitched paths which exhibit failover on the order of milliseconds, our experimental measurements show that interdomain routers in the pac ..."
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Cited by 408 (5 self)
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these periods of delayed convergence, we show that endtoend Internet paths will experience intermittent loss of connectivity, as well as increased packet loss and latency. We present a twoyear study of Internet routing convergence through the experimental instrumentation of key portions of the Internet
Lectures on the billiards
 In Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst
, 1974
"... These lectures together with the appendices contain all the essential steps for a proof of the ergodicity of the dynamical system described below as (M,T,v) or "periodic billiard's section ~ when the obstacles are so situated that no collisionless paths are possible. A point mass moves, w ..."
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Cited by 5 (0 self)
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These lectures together with the appendices contain all the essential steps for a proof of the ergodicity of the dynamical system described below as (M,T,v) or "periodic billiard's section ~ when the obstacles are so situated that no collisionless paths are possible. A point mass moves
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