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- Brendan Farrell, Yi Huang, Mark Iwen, Ting Wang, Lisa Zhang, Jintong Zheng
- 2007

We consider a flexible greedy approach to wavelength assignment in an optical network with the goal of minimizing the cost incurred by wavelength conversions and fiber deployment. The greedy approach processes demands one by one in a certain order and makes a locally optimal choice for each demand. We address several heuristics for creating desirable demand… (More)

- BRENDAN FARRELL
- 2012

We study invertibility of matrices of the form D + R where D is an arbitrary symmetric deterministic matrix, and R is a symmetric random matrix whose independent entries have continuous distributions with bounded densities. We show that (D + R) −1 = O(n 2) with high probability. The bound is completely independent of D. No moment assumptions are placed on… (More)

- Michael B. McCoy, Brendan Farrell, Andrea Reinhardt
- 2013

Let H be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on L p (H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α 1 I + S f , where S f is the operator given by convolution with f , f ∈ L 1 v (H), is invertible in B(L p… (More)

We derive an explicit lower bound on the capacity of the discrete amplitude–constrained Gaussian channel by proving the existence of tight frames that permit redundant vector representations with small coefficients. Our method encodes the information in subspaces that are optimal in terms of the power to amplitude ratio. In a recent paper, Lyubarskii and… (More)

We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order √ log n, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order log log n. This is a noteworthy difference to… (More)

We address the peak-to-average power ratio (PAPR) of transmission signals in OFDM and consider the performance of tone reservation for reduction of the PAPR. Tone reservation is unique among methods for reducing PAPR, because it does not affect information bearing coefficients and involves no additional coordination of transmitter and receiver. It is shown… (More)

Let H be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on L p (H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α 1 δ + f , f ∈ L 1 v (H), is invertible with respect to convolu-tion over H, then (α 1 δ + f) −1 = α 2 δ + g, g… (More)

Previous results on certain sampling series have left open if divergence only occurs for certain subsequences or, in fact, in the limit. Here we prove that divergence occurs in the limit. We consider three canonical reconstruction methods for functions in the Paley-Wiener space PW 1 π. For each of these we prove an instance when the reconstruction diverges… (More)