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by William Patrick, William Patrick , 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 High-Dimensional Configuration Spaces

by Lydia Kavraki, Petr Svestka, Jean-claude Latombe, Mark Overmars - 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 collision-free configurations and whose edg ..."
Abstract - Cited by 1277 (120 self) - Add to MetaCart
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

by David Andersen, Hari Balakrishnan, Frans Kaashoek, Robert Morris , 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 wide-area routing protocols that take at least several minutes to recover. A R ..."
Abstract - Cited by 1160 (31 self) - Add to MetaCart
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 wide-area routing protocols that take at least several minutes to recover. A

End-to-End Routing Behavior in the Internet

by Vern Paxson , 1996
"... The large-scale 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 end-to-end route measurements conducted using repeated “traceroutes” ..."
Abstract - Cited by 655 (13 self) - Add to MetaCart
, ” 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

End-to-End Internet Packet Dynamics,”

by Vern Paxson - Proc. SIGCOMM '97, , 1997
"... Abstract We discuss findings from a large-scale 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 end-to-end ..."
Abstract - Cited by 843 (19 self) - Add to MetaCart
-to-end behaviors due to the different directions of the Internet paths, which often exhibit asymmetries. We characterize the prevalence of unusual network events such as out-of-order delivery and packet corruption; discuss a robust receiver-based algorithm for estimating "bottleneck bandwidth

Billiards in Nearly Isosceles Triangles

by W. Patrick Hooper, Richard Evan Schwartz , 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 self-similarity phenomena in irrational triangu ..."
Abstract - Cited by 5 (1 self) - Add to MetaCart
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 self-similarity phenomena in irrational

End-to-end available bandwidth: Measurement methodology, dynamics, and relation with TCP throughput

by Manish Jain, Constantinos Dovrolis - In Proceedings of ACM SIGCOMM , 2002
"... The available bandwidth (avail-bw) in a network path is of major importance in congestion control, streaming applications, QoS verification, server selection, and overlay networks. We describe an end-to-end methodology, called Self-Loading Periodic Streams (SLoPS), for measuring avail-bw. The basic ..."
Abstract - Cited by 414 (20 self) - Add to MetaCart
The available bandwidth (avail-bw) in a network path is of major importance in congestion control, streaming applications, QoS verification, server selection, and overlay networks. We describe an end-to-end methodology, called Self-Loading Periodic Streams (SLoPS), for measuring avail-bw. The basic

Obtuse Triangular Billiards II: 100 Degrees Worth of Periodic Trajectories

by Richard Evan Schwartz
"... We give a rigorous computer-assisted 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 ..."
Abstract - Cited by 9 (1 self) - Add to MetaCart
We give a rigorous computer-assisted 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

by Craig Labovitz, Abha Ahuja, Abhijit Bose, Farnam Jahanian - 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 circuit-switched paths which exhibit failover on the order of milliseconds, our experimental mea-surements show that interdomain routers in the pac ..."
Abstract - Cited by 408 (5 self) - Add to MetaCart
these periods of delayed convergence, we show that end-to-end Internet paths will experience intermittent loss of connectivity, as well as increased packet loss and latency. We present a two-year study of Internet routing convergence through the experimental instrumentation of key portions of the Internet

Lectures on the billiards

by Giovanni Gallavotti - In Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst , 1974
"... These lectures together with the appendices contain all the es-sential 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 ..."
Abstract - Cited by 5 (0 self) - Add to MetaCart
These lectures together with the appendices contain all the es-sential 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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