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- Aran Nayebi
- 2009

On distributed memory electronic computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to demonstrate the theoretical encoding of Strassen's fast matrix multiplication algorithm with DNA based on an n-moduli set in… (More)

Given a random permutation f : [N ] → [N ] as a black box and y ∈ [N ], we want to output x = f −1 (y). Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on the permutation but not on the input y. Classically, there is a data structure of size˜O(S) and an algorithm that with the… (More)

- Aran Nayebi, Matt Vitelli
- 2015

We compare the performance of two different types of recurrent neural networks (RNNs) for the task of algorithmic music generation, with audio waveforms as input. In particular, we focus on RNNs that have a sophisticated gating mechanism , namely, the Long Short-Term Memory (LSTM) network and the recently introduced Gated Recurrent Unit (GRU). Our results… (More)

We consider the quantum time complexity of the all pairs shortest paths (APSP) problem and some of its variants. The trivial classical algorithm for APSP and most all pairs path problems runs in O(n 3) time, while the trivial algorithm in the quantum setting runs iñ O(n 2.5) time, using Grover search. A major open problem in classical algorithms is to… (More)

For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to… (More)

- Aran Nayebi
- ArXiv
- 2012

- Aran Nayebi
- 2009

Let R k (n) be the number of representations of an integer n as the sum of a prime and a k-th power for k ≥ 2. Furthermore, set E k (X) = |{n ≤ X, n ∈ I k , n not a sum of a prime and a k-th power}|. In the present paper we use sieve techniques to obtain a strong upper bound on R k (n) for n ≤ X with no exceptions, and we improve upon the results of A.… (More)

- Aran Nayebi
- ArXiv
- 2009

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