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A VLSI architecture and layout for a convolutional encoder is described. This architecture allows a single chip implementation of an encoder that is capable of handling many different convolutional codes including all the convolutional codes that are presently used for deep space missions.
Cubic convolution, which has been discussed by Rifman and McKinnon (1974), was originally developed for the reconstruction of Landsat digital images. In the present investigation, the reconstruction properties of the one-parameter family of cubic convolution interpolation functions are considered and thee image degradation associated with reasonable choices of this parameter is analyzed. With the aid of an analysis in the frequency domain it is demonstrated that in an image-independent sense there is an optimal value for this parameter. The optimal value is not the standard value commonly referenced in the literature. It is also demonstrated that in an image-dependent sense, cubic convolution can be adapted to any class of images characterized by a common energy spectrum.
An error-trellis syndrome decoding technique for convolutional codes is developed. This algorithm is then applied to the entire class of systematic convolutional codes and to the high-rate, Wyner-Ash convolutional codes. A special example of the one-error-correcting Wyner-Ash code, a rate 3/4 code, is treated. The error-trellis syndrome decoding method applied to this example shows in detail how much more efficient syndrome decoding is than Viterbi decoding if applied to the same problem. For standard Viterbi decoding, 64 states are required, whereas in the example only 7 states are needed. Also, within the 7 states required for decoding, many fewer transitions are needed between the states.
An error-trellis syndrome decoding technique for convolutional codes is developed. This algorithm is then applied to the entire class of systematic convolutional codes and to the high-rate, Wyner-Ash convolutional codes. A special example of the one-error-correcting Wyner-Ash code, a rate 3/4 code, is treated. The error-trellis syndrome decoding method applied to this example shows in detail how much more efficient syndrome decordig is than Viterbi decoding if applied to the same problem. For standard Viterbi decoding, 64 states are required, whereas in the example only 7 states are needed. Also, within the 7 states required for decoding, many fewer transitions are needed between the states.
Maximum Likelihood Convolutional Decoding, which is used by the Deep Space Network for short constraint-length convolutional codes, assumes that all strings of information bits are equally likely. In some cases, like image data, this is not the case. The use of information about an adjacent pixel in decoding convolutionally encoded Voyager images is examined. It is discovered that, in a region of interest, as much as 2 dB may be gained.
Machine vision and image recognition require sophisticated image processing prior to the application of Artificial Intelligence. Two Dimensional Convolute Integer Technology is an innovative mathematical approach for addressing machine vision and image recognition. This new technology generates a family of digital operators for addressing optical images and related two dimensional data sets. The operators are regression generated, integer valued, zero phase shifting, convoluting, frequency sensitive, two dimensional low pass, high pass and band pass filters that are mathematically equivalent to surface fitted partial derivatives. These operators are applied non-recursively either as classical convolutions (replacement point values), interstitial point generators (bandwidth broadening or resolution enhancement), or as missing value calculators (compensation for dead array element values). These operators show frequency sensitive feature selection scale invariant properties. Such tasks as boundary/edge enhancement and noise or small size pixel disturbance removal can readily be accomplished. For feature selection tight band pass operators are essential. Results from test cases are given.
Decoding results are described for long decoding runs of Galileo's convolutional codes. A 1 k-bit/sec hardware Viterbi decoder is used for the (15, 1/4) convolutional code, and a software Viterbi decoder is used for the (7, 1/2) convolutional code. The output data of these long runs are stored in data files using a data compression format which can reduce file size by a factor of 100 to 1 typically. These data files can be used to replicate the long, time-consuming runs exactly and are useful to anyone who wants to analyze the burst statistics of the Viterbi decoders. The 1 k-bit/sec hardware Viterbi decoder was developed in order to demonstrate the correctness of certain algorithmic concepts for decoding Galileo's experimental (15, 1/4) code, and for the long-constraint-length codes in general. The hardware decoder can be used both to search for good codes and to measure accurately the performance of known codes.
A determinate state convolutional code is formed from a conventional convolutional code by pruning away some of the possible state transitions in the decoding trellis. The type of staged power transfer used in determinate state convolutional codes proves to be an extremely efficient way of enhancing the performance of a concatenated coding system. The decoder complexity is analyzed along with free distances of these new codes and extensive simulation results is provided of their performance at the low signal to noise ratios where a real communication system would operate. Concise, practical examples are provided.
In this paper we describe a novel generalized SOR (successive overrelaxation) algorithm for accelerating the convergence of the dynamic iteration method known as waveform relaxation. A new convolution SOR algorithm is presented, along with a theorem for determining the optimal convolution SOR parameter. Both analytic and experimental results are given to demonstrate that the convergence of the convolution SOR algorithm is substantially faster than that of the more obvious frequency-independent waveform SOR algorithm. Finally, to demonstrate the general applicability of this new method, it is used to solve the differential-algebraic system generated by spatial discretization of the time-dependent semiconductor device equations.
There exist almost complete convolutional encodings of self-dual codes, i.e., block codes of rate 1/2 with weights w, w = 0 mod 4. The codes are of length 8m with the convolutional portion of length 8m-2 and the nonsystematic information of length 4m-1. The last two bits are parity checks on the two (4m-1) length parity sequences. The final information bit complements one of the extended parity sequences of length 4m. Solomon and van Tilborg have developed algorithms to generate these for the Quadratic Residue (QR) Codes of lengths 48 and beyond. For these codes and reasonable constraint lengths, there are sequential decodings for both hard and soft decisions. There are also possible Viterbi-type decodings that may be simple, as in a convolutional encoding/decoding of the extended Golay Code. In addition, the previously found constraint length K = 9 for the QR (48, 24;12) Code is lowered here to K = 8.
Solomon and van Tilborg have developed convolutional encoding algorithms for quadratic residue (QR) codes of lengths 47 and beyond. For these codes and reasonable constraint lengths, there are sequential decodings that may be simple, as in a convolutional encoding/decoding of the extended Golay Code. In addition, the previously found constraint length K = 9 for the (48, 24; 12) QR code was lower to K = 8 by Solomon. In our search for the smallest possible constraint lengths K for (80, 40; 16) self-dual quadratic residue and nonquadratic residue codes, we have found the constraint lengths K = 14 and K = 13, respectively. We have discovered a K = 21 convolutional encoding for the (104, 52; 20) QR code; there may be a smaller K for a (104, 52; 20) self-dual code that is not a quadratic residue code. The smaller the K, the less complex the sequential or Viterbi decoder.
Traditional knowledge graphs tend to be too generic, and often perform poorly on complex scientific queries. Often times, precedence is given to pop culture over scientific knowledge for queries. This is predominantly due to the use of internet sources for building the knowledge graph. With this work, we aim to explore the effectiveness of combining a knowledge graph generated from earth science corpora with a language model and graph convolutions for the purpose of surfacing latent and related sentences given a natural language query. In this model, sentences are conceptualized in the graph as nodes which are connected through entities—words and phrases of interest found in the text—extracted using Google Cloud’s entity extraction model. The language model we used for this is Bidirectional Encoder Representations from Transformers (BERT).The sentences are given a numeric representation by the BERT model. Graph convolutions are then applied to sentence embeddings in order to obtain a vector representation of the sentence as well as the surrounding graph structure, thereby leveraging the power of adjacency inherently encoded in graph structures. With this presentation, we demonstrate the ability of graph convolutions and their improved ability to surface relevant, latent information based on the subject of the input query.
Graph Convolutional Neural Networks (GCNNs) have emerged as powerful tools for analyzing materials. In this study, we employ GCNNs to examine structural characteristics of CuZr metallic glasses (MGs) and identify their states. We use molecular dynamics to simulate the quenching process of CuZr, using cooling rates ranging from 10 9 to 10 15 K/s, to produce six unique glassy states. For each state, we create a dataset comprising 1,800 distinct samples. We evaluate the effectiveness of various GCNNs, including Graph Attention Neural Network (GANN), Graph Sample and AggreGatE (GraphSAGE), Graph Isomorphism Network (GIN), and Relational Graph Convolutional Neural Network (RGCN). GANN and GraphSAGE demonstrate comparable performance, achieving an overall accuracy of 81% in classifying the MG states. Furthermore, these results underscore the potential of GCNNs to detect subtle structural variances in disordered materials and point to broader application of deep learning in the analysis of MGs and other amorphous substances.
Principles of materials science and engineering, physics, mathematics, and information science are used to extract knowledge and insights from the process-structure–property-performance relationships hidden in materials data. The process-structure modeling can be accelerated without loss of interpretability, with artificial intelligence tools that mimic the salient features of the process and process-structure relations. In this work, a novel convoluted model-filtering technique was exploited to build and successfully train the Convoluted Filter (CoFi) artifacts for Fe-based alloy heat treatment cycles. The artifacts were pre-trained to filter out deep models that change the surrogate microstructure state after the heat treatment at ambient conditions. Direct representation of the thermal cycle features within knowledge Graph facilitated development of meaningful data models for microstructure evolution, which reduce overfitting to limited datasets.
Herein we propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer learning. The method provides an adaptive, hierarchical architecture that capitalizes on a progressive training approach for multiscale spatio-temporal data. This framework allows for inputs across multiple scales: starting from a compact (small number of weights) network architecture and low-resolution data, our network progressively deepens and widens itself in a principled manner to encode new information in the higher resolution data based on its current performance of reconstruction. Basic transfer learning techniques are applied to ensure information learned from previous training steps can be rapidly transferred to the larger network. As a result, the network can dynamically capture different scaled features at different depths of the network. The performance gains of this adaptive multiscale architecture are illustrated through a sequence of numerical experiments on synthetic examples and real-world spatial-temporal data.
Simulating nuclear reactor cores at the highest achievable spatial and energy resolution is critical in modeling these systems accurately. Increasing the resolution, however, can dramatically increase the memory and central processing unit time required to run simulations. A convolutional neural network was shown previously to accurately upsample tally results of simulated light water reactor assemblies fueled with fresh, low enriched uranium. Here, we show that a convolutional neural network can be used to upsample tally results in assemblies containing fresh and depleted fuel enriched from 1.6 to 19.9 atom percent. The network was trained using neutron flux tallies from simulations of light water reactor assemblies with a range of fuel and coolant temperatures and a diverse selection of geometries. Accurate predictions of flux tallies are possible even on test assemblies with geometries and burnup levels well outside the range of those present in the training and validation data. The network improves the data density by a factor of 8 over a broad range of light water reactor assemblies while incurring insignificant additional computational cost to a Monte Carlo simulation.
We study the 2D Orszag–Tang vortex magnetohydrodynamics (MHD) problem through the use of physics-constrained convolutional neural networks (PCNNs) for forecasting the density, ρ, and the magnetic field, B, as well as the prediction of B given the velocity field v of the fluid. In addition to translation equivariance from the convolutional architecture, other physics constraints were embedded: absence of magnetic monopoles, non-negativity of ρ, use of only relevant variables, and the periodic boundary conditions of the problem. The use of only relevant variables and the hard constraint of non-negative ρ were found to facilitate learning greatly. The divergenceless condition ∇·B=0 was implemented as a hard constraint up to machine precision through the use of a magnetic potential to define B=∇×A. Residual networks and data augmentation were also used to improve performance. This allowed for some of the residual models to function as surrogate models and provide reasonably accurate simulations. For the prediction task, the PCNNs were evaluated against a physics-informed neural network, which had the ideal MHD induction equation as a soft constraint. Several models were able to generate highly accurate fields, which are visually almost indistinguishable and have low mean squared error. Only methods with built-in hard constraints produced physical fields with ∇·B=0. The use of PCNNs for MHD has the potential to produce physically consistent real-time simulations to serve as virtual diagnostics in cases where inferences must be made with limited observables.
Abstract We identify and investigate the origin and nature of the transition between Gaussian and exponential forms of decoherence: the decoherence factor (that controls the time dependence of the off-diagonal terms of the density matrix expressed in the pointer basis representation) is the convolution of the Fourier transforms of the spectral density and of the overlap (between the eigenstates the environment with and without couplings to the system). Spectral density alone tends to lead to the (approximately) Gaussian decay of coherence while the overlap alone results in a (largely) exponential decay. We show that these two contributions combine as a convolution, their relative importance controlled by the strength of the system-environment coupling. The resulting decoherence factor in the strong and weak coupling limits leads to predominantly Gaussian or exponential decay, respectively, as is demonstrated with two paradigmatic examples of decoherence—a spin-bath model and the quantum Brownian motion.