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The Cell Broadband Enginee (Cell/B.E.) processor is the first implementation of the Cell Broadband Engine Architecture (CBEA), developed jointly by Sony, Toshiba, and IBM. In addition to use of the Cell/B.E. processor in the Sony Computer Entertainment PLAYSTATIONt3 system, there is much interest in using it for workstations, media-rich electronics devices,(More)
  • Thomas Chen, Nataša Pavlovi´c, Schlein-Yau, Klainerman-Machedon, Kirkpatrick-Schlein-Staffilani
  • 2008
We investigate the dynamics of a boson gas with three-body interactions in dimensions d = 1, 2. We prove that in the limit where the particle number N tends to infinity, the BBGKY hierarchy of k-particle marginals converges to a limiting (Gross-Pitaevskii (GP)) hierarchy for which we prove existence and uniqueness of solutions. The solutions of the GP(More)
We derive the defocusing cubic Gross-Pitaevskii (GP) hierarchy in dimensions d = 2, 3, from an N-body Schrödinger equation describing a gas of interacting bosons in the GP scaling, in the limit N → ∞. The main result of this paper is the proof of convergence of the corresponding BBGKY hierarchy to a GP hierarchy in the spaces introduced in our previous work(More)
We consider the dynamical Gross-Pitaevskii (GP) hierarchy on R d , d ≥ 1, for cubic, quintic, focusing and defocusing interactions. For both the focusing and defocusing case, and any d ≥ 1, we prove local wellposedness of the Cauchy problem in weighted Sobolev spaces H α ξ of sequences of marginal density matrices, for α 8 > < > : > 1 2 if d = 1 > d 2 − 1(More)
We consider solutions of the focusing cubic and quintic Gross-Pitaevskii (GP) hierarchies. We identify an observable corresponding to the average energy per particle, and we prove that it is a conserved quantity. We prove that all solutions to the focusing GP hierarchy at the L 2-critical or L 2-supercritical level blow up in finite time if the energy per(More)
  • T Chen, N Pavlovi´c, N Tzirakis
  • 2011
This article consists of two parts. In the first part, we review the most recent proofs establishing quadratic Morawetz inequalities for the nonlinear Schrödinger equation (NLS). We also describe the applications of these estimates to the problem of quantum scattering. In the second part, we generalize some of the methods developed for the NLS by many(More)
Designing NoC-based systems has become increasingly complex with support for multiple functionalities. Decisions regarding interconnections between the heterogeneous system components and routing of system communication affect system performance and power consumption. This research provides a heuristic to determine the neighborhood configuration for each(More)
— Measurements of high-speed network traffic have shown that traffic data exhibits a high degree of self-similarity. Traditional traffic models such as AR and ARMA are not able to capture this long-range-dependence making them ineffective for the traffic prediction task. In this paper, we apply the fractional ARIMA (F-ARIMA) model to predict one-step-ahead(More)
A sparse coding ASIC is designed to learn visual receptive fields and infer the sparse representation of images for encoding, feature detection and recognition. 256 leaky integrate-and-fire neurons are connected in a 2-layer network of 2D local grids linked in a 4-stage systolic ring to reduce the communication latency. Spike collisions are kept sparse(More)
—Sparse coding encodes natural stimuli using a small number of basis functions known as receptive fields. In this work, we design custom hardware architectures for efficient and high-performance implementations of a sparse coding algorithm called the sparse and independent local network (SAILnet). A study of the neuron spiking dynamics uncovers important(More)