Turing machines can be efficiently simulated by the General Purpose Analog Computer

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity level, by showing that, modulo polynomial reductions, computations of Turing machines can be simulated by GPACs, without the need of using more (space) resources than those used in the original Turing computation, as long as we are talking about bounded computations. In other words, computations done by the GPAC are as space-efficient as computations done in the context of Computable Analysis

Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546

A Hierarchical Classification of First-Order Recurrent Neural Networks

We provide a decidable hierarchical classification of first-order recurrent neural networks made up of McCulloch and Pitts cells. This classification is achieved by proving an equivalence result between such neural networks and deterministic Buuchi automata, and then translating the Wadge classification theory from the abstract machine to the neural network context. The obtained hierarchy of neural networks is proved to have width 2 and height omega + 1, and a decidability procedure of this hierarchy is provided. Notably, this classification is shown to be intimately related to the attractive properties of the considered networks

Adaptive multi-modal sensors

Compressing real-time input through bandwidth constrainedconnections has been studied within robotics, wireless sensor networks,and image processing. When there are bandwidth constraints on real-time input the amount of information to be transferred will always begreater than the amount that can be transferred per unit of time. Wepropose a system that utilizes a local diffusion process and a reinforcement learning-based memory system to establish a realtime predictionof an entire input space based upon partial observation. The proposedsystem is optimized for dealing with multi-dimension input spaces, andmaintains the ability to react to rare events. Results show the relationof loss to quality and suggest that at higher resolutions gains in qualityare possible

Emotions for Strategic Real-Time Systems

Strategie real-time systems are of high potential and their applications are growing, although they are mostly prevalent in video games, military training, and military planning. We propose a paradigm to advance current systems by introducing emotions into the simulated agents that make decisions and solve situations cooperatively. By utilizing emotional reactions and communication, we hope to advance these systems so that the decision process better mimics human behavior. Since our system allows sharing of emotions with nearby agents it utilizes both internal and external emotional control