We propose an optical computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible subsets of the given set. To each arc we assign either a number from the given set or a predefined constant. When the light is passing through an arc it is delayed by the amount of time indicated by the number placed in that arc. At the destination node we will check if there is a ray whose total delay is equal to the target value of the subset sum problem (plus some constants). The proposed optical solution solves a NP-complete problem in time proportional with the target sum, but requires an exponential amount of energy.
Naughton (et al) proposed and investigated @cite_14 @cite_2 a model called the continuous space machine which operates in discrete time-steps over a number of two-dimensional complex-valued images of constant size and arbitrary spatial resolution. The (constant time) operations on images include Fourier transformation, multiplication, addition, thresholding, copying and scaling.
@cite_14 @cite_2
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We prove computability and complexity results for an original model of computation called the continuous space machine. Our model is inspired by the theory of Fourier optics. We prove our model can simulate analog recurrent neural networks, thus establishing a lower bound on its computational power. We also define a Θ(log2n) unordered search algorithm with our model. We introduce a volumetric space-time technique for the reconstruction of moving and deforming objects from point data. The output of our method is a four-dimensional space-time solid, made up of spatial slices, each of which is a three-dimensional solid bounded by a watertight manifold. The motion of the object is described as an incompressible flow of material through time. We optimize the flow so that the distance material moves from one time frame to the next is bounded, the density of material remains constant, and the object remains compact. This formulation overcomes deficiencies in the acquired data, such as persistent occlusions, errors, and missing frames. We demonstrate the performance of our flow-based technique by reconstructing coherent sequences of watertight models from incomplete scanner data. A basic and extensive treatment of discrete aspects of the scale-space theory is presented. A genuinely discrete scale-space theory is developed and its connection to the continuous scale-space theory is explained. Special attention is given to discretization effects, which occur when results from the continuous scale-space theory are to be implemented computationally. The 1D problem is solved completely in an axiomatic manner. For the 2D problem, the author discusses how the 2D discrete scale space should be constructed. The main results are as follows: the proper way to apply the scale-space theory to discrete signals and discrete images is by discretization of the diffusion equation, not the convolution integral; the discrete scale space obtained in this way can be described by convolution with the kernel, which is the discrete analog of the Gaussian kernel, a scale-space implementation based on the sampled Gaussian kernel might lead to undesirable effects and computational problems, especially at fine levels of scale; the 1D discrete smoothing transformations can be characterized exactly and a complete catalogue is given; all finite support 1D discrete smoothing transformations arise from repeated averaging over two adjacent elements (the limit case of such an averaging process is described); and the symmetric 1D discrete smoothing kernels are nonnegative and unimodal, in both the spatial and the frequency domain. > In this paper, we generate two computational models in order to estimate two dominant global properties (naturalness and openness) for representing a scene based on its global spatial structure. Naturalness and openness are two dominant perceptual properties within a multidimensional space in which semantically similar scenes (e.g., corridor and hallway) are assigned to nearby points. In this model space, the representation of a real-world scene is based on the overall shape of a scene but not on local object information. We introduce the use of a deep convolutional neural network for generating features that are well-suited for estimating the two global properties of a visual scene. The extracted features are integrated in an efficient way and fed into a linear support vector machine (SVM) to classify naturalness versus man-madeness and openness versus closedness. These two global properties (naturalness and openness) of an input image can be predicted from activations in the lowest layer of the convolutional neural network which has been trained for a scene recognition task. The consistent results of computational models in full and restricted spatial frequency ranges suggest that the representation of an image in the lowest layer of the deep scene CNN contains holistic information of the images as it leads to highest accuracy in modelling the global shape of the scene.