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228,815
RealTime Systems
, 2000
"... Collision avoidance is an important topic in multirobot systems. Existing multirobot pathfinding approaches ignore sideswipe collisions among robots (i.e., only consider the collision which two agents try to occupy the same node during the same timestep) [1, 3, 4], and allow diagonal move between ..."
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Cited by 602 (11 self)
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between robots R1 and R2 in the situation depicted in Figure 1(a), but also that in Figure 1(b), which is typically not considered as a collision in existing multirobot systems. (a) (b) (c) Figure 2: Illustration of deadloop. The green square and the red square are the robot positions and the goal
Modular elliptic curves and Fermat’s Last Theorem
 ANNALS OF MATH
, 1995
"... When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c n ..."
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Cited by 617 (2 self)
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When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
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Cited by 879 (14 self)
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‖ˆx − x ‖ 2 ℓ2 ≤ C2 ( · 2 log p · σ 2 + ∑ min(x 2 i, σ 2) Our results are nonasymptotic and we give values for the constant C. In short, our estimator achieves a loss within a logarithmic factor of the ideal mean squared error one would achieve with an oracle which would supply perfect information
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 540 (59 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 558 (0 self)
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space is not σfinite. p. 13: add after I.2.6.16: I.2.6.17. If X is a compact subset of C not containing 0, and k ∈ N, there is in general no bound on the norm of T −1 as T ranges over all operators with ‖T ‖ ≤ k and σ(T) ⊆ X. For example, let Sn ∈ L(l 2) be the truncated shift: Sn(α1, α2,...) = (0
Measuring individual differences in implicit cognition: The implicit association test
 J PERSONALITY SOCIAL PSYCHOL 74:1464–1480
, 1998
"... An implicit association test (IAT) measures differential association of 2 target concepts with an attribute. The 2 concepts appear in a 2choice task (e.g., flower vs. insect names), and the attribute in a 2nd task (e.g., pleasant vs. unpleasant words for an evaluation attribute). When instructions ..."
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Cited by 1008 (63 self)
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An implicit association test (IAT) measures differential association of 2 target concepts with an attribute. The 2 concepts appear in a 2choice task (e.g., flower vs. insect names), and the attribute in a 2nd task (e.g., pleasant vs. unpleasant words for an evaluation attribute). When instructions
Understanding packet delivery performance in dense wireless sensor networks
, 2003
"... Wireless sensor networks promise finegrain monitoring in a wide variety of environments. Many of these environments (e.g., indoor environments or habitats) can be harsh for wireless communication. From a networking perspective, the most basic aspect of wireless communication is the packet delivery ..."
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Cited by 661 (15 self)
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different environments:an indoor office building, a habitat with moderate foliage, and an open parking lot. Our findings have interesting implications for the design and evaluation of routing and mediumaccess protocols for sensor networks. Categories and Subject Descriptors C.2.1 [Network Architecture
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 873 (26 self)
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perfectly recover most lowrank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m ≥ C n 1.2 r log n for some positive numerical constant C, then with very high probability, most n × n matrices of rank r can be perfectly recovered
Active Messages: a Mechanism for Integrated Communication and Computation
, 1992
"... The design challenge for largescale multiprocessors is (1) to minimize communication overhead, (2) allow communication to overlap computation, and (3) coordinate the two without sacrificing processor cost/performance. We show that existing message passing multiprocessors have unnecessarily high com ..."
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Cited by 1054 (75 self)
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tremendous flexibility. Implementations on nCUBE/2 and CM5 are described and evaluated using a splitphase sharedmemory extension to C, SplitC. We further show that active messages are sufficient to implement the dynamically scheduled languages for which message driven machines were designed
An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any po ..."
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Cited by 984 (32 self)
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query point q 2 R d , and ffl ? 0, a (1 + ffl)approximate nearest neighbor of q can be computed in O(c d;ffl log n) time, where c d;ffl d d1 + 6d=ffle d is a factor depending only on dimension and ffl. In general, we show that given an integer k 1, (1 + ffl)approximations to the k nearest neighbors
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