Aran Nayebi

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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)
A central challenge in sensory neuroscience is to understand neural computations and circuit mechanisms that underlie the encoding of ethologically relevant, natural stimuli. In multilayered neural circuits, nonlinear processes such as synaptic transmission and spiking dynamics present a significant obstacle to the creation of accurate computational models(More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract 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(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)
Consider a source that emits a sequence of symbols U 1 , U (independently and identically distributed) according to the probability mass function P (U = a) = 0.7 P (U = b) = P (U = c) = 0.15 Our task is to encode the source sequence into binary bits (1s and 0s). How should we do so? The naive way is to use two bits to represent each symbol, since there are(More)