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The purpose of this paper is to prove a conjecture made by Stephen Wolfram in 1985, that an elementary one dimensional cellular automaton known as " Rule 110 " is capable of universal computation. I developed this proof of his conjecture while assisting Stephen Wolfram on research for A New Kind of Science [1]. The purpose of this paper is to prove that one(More)
We investigate the power of the Wang tile self-assembly model at temperature 1, a threshold value that permits attachment between any two tiles that share even a single bond. When restricted to deterministic assembly in the plane, no temperature 1 assembly system has been shown to build a shape with a tile complexity smaller than the diameter of the shape.(More)
In order to understand how the mammalian neocortex is performing computations, two things are necessary; we need to have a good understanding of the available neuronal processing units and mechanisms, and we need to gain a better understanding of how those mechanisms are combined to build functioning systems. Therefore, in recent years there is an(More)
— Recent development of neuromorphic hardware offers great potential to speed up simulations of neural networks. SpiNNaker is a neuromorphic hardware and software system designed to be scalable and flexible enough to implement a variety of different types of simulations of neural systems, including spiking simulations with plasticity and learning.(More)
A highly desired part of the synthetic biology toolbox is an embedded chemical microcontroller, capable of autonomously following a logic program specified by a set of instructions, and interacting with its cellular environment. Strategies for incorporating logic in aqueous chemistry have focused primarily on implementing components, such as logic gates,(More)
—Deep neural networks such as Convolutional Networks (ConvNets) and Deep Belief Networks (DBNs) represent the state-of-the-art for many machine learning and computer vision classification problems. To overcome the large computational cost of deep networks, spiking deep networks have recently been proposed , given the specialized hardware now available for(More)
Much work has been done to understand when given predicates (relations) on discrete variables can be con-joined to implement other predicates. Indeed, the lattice of " co-clones " (sets of predicates closed under conjunction , variable renaming, and existential quantifica-tion of variables) has been investigated steadily from the 1960's to the present.(More)
— Models of ad-hoc wireless networks are often based on the geometric disc abstraction: transmission is assumed to be isotropic, and reliable communication channels are assumed to exist (apart from interference) between nodes closer than a given distance. In reality communication channels are unreliable and communication range is generally not rotationally(More)