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Hybrid computers are computers that exhibit features of analog computers and digital computers. The digital component normally serves as the controller and provides logical and numerical operations, while the analog component often serves as a solver of differential equations and other mathematically complex problems.
The first desktop hybrid computing system was the Hycomp 250, released by Packard Bell in 1961. [1] Another early example was the HYDAC 2400, an integrated hybrid computer released by EAI in 1963. [2] In the 1980s, Marconi Space and Defense Systems Limited (under Peggy Hodges) developed their "Starglow Hybrid Computer", which consisted of three EAI 8812 analog computers linked to an EAI 8100 digital computer, the latter also being linked to an SEL 3200 digital computer. [3] Late in the 20th century, hybrids dwindled with the increasing capabilities of digital computers including digital signal processors. [4]
In general, analog computers are extraordinarily fast, since they are able to solve most mathematically complex equations at the rate at which a signal traverses the circuit, which is generally an appreciable fraction of the speed of light. On the other hand, the precision of analog computers is not good; they are limited to three, or at most, four digits of precision.
Digital computers can be built to take the solution of equations to almost unlimited precision, but quite slowly compared to analog computers. Generally, complex mathematical equations are approximated using iterative methods which take huge numbers of iterations, depending on how good the initial "guess" at the final value is and how much precision is desired. (This initial guess is known as the numerical "seed".) For many real-time operations in the 20th century, such digital calculations were too slow to be of much use (e.g., for very high frequency phased array radars or for weather calculations), but the precision of an analog computer is insufficient.
Hybrid computers can be used to obtain a very good but relatively imprecise 'seed' value, using an analog computer front-end, which is then fed into a digital computer iterative process to achieve the final desired degree of precision. With a three or four digit, highly accurate numerical seed, the total digital computation time to reach the desired precision is dramatically reduced, since many fewer iterations are required. One of the main technical problems to be overcome in hybrid computers is minimizing digital-computer noise in analog computing elements and grounding systems.
Consider that the nervous system in animals is a form of hybrid computer. Signals pass across the synapses from one nerve cell to the next as discrete (digital) packets of chemicals, which are then summed within the nerve cell in an analog fashion by building an electro-chemical potential until its threshold is reached, whereupon it discharges and sends out a series of digital packets to the next nerve cell. The advantages are at least threefold: noise within the system is minimized (and tends not to be additive), no common grounding system is required, and there is minimal degradation of the signal even if there are substantial differences in activity of the cells along a path (only the signal delays tend to vary). The individual nerve cells are analogous to analog computers; the synapses are analogous to digital computers.
Hybrid computers are distinct from hybrid systems. The latter may be no more than a digital computer equipped with an analog-to-digital converter at the input and/or a digital-to-analog converter at the output, to convert analog signals for ordinary digital signal processing, and conversely, e.g., for driving physical control systems, such as servomechanisms.
In 2015, researchers at Columbia University published a paper [5] on a small scale hybrid computer in 65 nm CMOS technology. This 4th-order VLSI hybrid computer contains 4 integrator blocks, 8 multiplier/gain-setting blocks, 8 fanout blocks for distributing current-mode signals, 2 ADCs, 2 DACs and 2 SRAMs blocks. Digital controllers are also implemented on the chip for executing the external instructions. A robot experiment in the paper demonstrates the use of the hybrid computing chip in today's emerging low-power embedded applications.
An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude.
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics, numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.
In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals.
In electronics, a digital-to-analog converter is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The IEEE Transactions on Signal Processing includes audio, video, speech, image, sonar, and radar as examples of signals. A signal may also be defined as any observable change in a quantity over space or time, even if it does not carry information.
Neuromorphic computing is an approach to computing that is inspired by the structure and function of the human brain. A neuromorphic computer/chip is any device that uses physical artificial neurons to do computations. In recent times, the term neuromorphic has been used to describe analog, digital, mixed-mode analog/digital VLSI, and software systems that implement models of neural systems. The implementation of neuromorphic computing on the hardware level can be realized by oxide-based memristors, spintronic memories, threshold switches, transistors, among others. Training software-based neuromorphic systems of spiking neural networks can be achieved using error backpropagation, e.g., using Python based frameworks such as snnTorch, or using canonical learning rules from the biological learning literature, e.g., using BindsNet.
In numerical analysis, adaptive mesh refinement (AMR) is a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time the solution is being calculated. When solutions are calculated numerically, they are often limited to pre-determined quantified grids as in the Cartesian plane which constitute the computational grid, or 'mesh'. Many problems in numerical analysis, however, do not require a uniform precision in the numerical grids used for graph plotting or computational simulation, and would be better suited if specific areas of graphs which needed precision could be refined in quantification only in the regions requiring the added precision. Adaptive mesh refinement provides such a dynamic programming environment for adapting the precision of the numerical computation based on the requirements of a computation problem in specific areas of multi-dimensional graphs which need precision while leaving the other regions of the multi-dimensional graphs at lower levels of precision and resolution.
Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI, depending on the complexity of the domain and the type of mesh desired. A typical goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable. The mesh should also be fine in areas that are important for the subsequent calculations.
VisSim is a visual block diagram program for simulation of dynamical systems and model-based design of embedded systems, with its own visual language. It is developed by Visual Solutions of Westford, Massachusetts. Visual Solutions was acquired by Altair in August 2014 and its products have been rebranded as Altair Embed as a part of Altair's Model Based Development Suite. With Embed, you can develop virtual prototypes of dynamic systems. Models are built by sliding blocks into the work area and wiring them together with the mouse. Embed automatically converts the control diagrams into C-code ready to be downloaded to the target hardware.
Unconventional computing is computing by any of a wide range of new or unusual methods. It is also known as alternative computing.
HRS-100, ХРС-100, GVS-100 or ГВС-100, was a third generation hybrid computer developed by Mihajlo Pupin Institute and engineers from USSR in the period from 1968 to 1971. Three systems HRS-100 were deployed in Academy of Sciences of USSR in Moscow and Novosibirsk (Akademgorodok) in 1971 and 1978. More production was contemplated for use in Czechoslovakia and German Democratic Republic (DDR), but that was not realised.
Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science.
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm is as efficient as possible.
Models of neural computation are attempts to elucidate, in an abstract and mathematical fashion, the core principles that underlie information processing in biological nervous systems, or functional components thereof. This article aims to provide an overview of the most definitive models of neuro-biological computation as well as the tools commonly used to construct and analyze them.
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is a matrix-free method for finding the largest eigenvalues and the corresponding eigenvectors of a symmetric generalized eigenvalue problem
A mesh is a representation of a larger geometric domain by smaller discrete cells. Meshes are commonly used to compute solutions of partial differential equations and render computer graphics, and to analyze geographical and cartographic data. A mesh partitions space into elements over which the equations can be solved, which then approximates the solution over the larger domain. Element boundaries may be constrained to lie on internal or external boundaries within a model. Higher-quality (better-shaped) elements have better numerical properties, where what constitutes a "better" element depends on the general governing equations and the particular solution to the model instance.
An AI accelerator is a class of specialized hardware accelerator or computer system designed to accelerate artificial intelligence and machine learning applications, including artificial neural networks and machine vision. Typical applications include algorithms for robotics, Internet of Things, and other data-intensive or sensor-driven tasks. They are often manycore designs and generally focus on low-precision arithmetic, novel dataflow architectures or in-memory computing capability. As of 2018, a typical AI integrated circuit chip contains billions of MOSFET transistors. A number of vendor-specific terms exist for devices in this category, and it is an emerging technology without a dominant design.
Validated numerics, or rigorous computation, verified computation, reliable computation, numerical verification is numerics including mathematically strict error evaluation, and it is one field of numerical analysis. For computation, interval arithmetic is used, and all results are represented by intervals. Validated numerics were used by Warwick Tucker in order to solve the 14th of Smale's problems, and today it is recognized as a powerful tool for the study of dynamical systems.
