A Ptolemaic framework for computer program complexes
Ptolemaic framework for computer program complexes
LOGIC NETWORK↗
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Application of advanced grid generation techniques for flow field computations about complex configurations
In the computation of flowfields about complex configurations, it is very difficult to construct a boundary-fitted coordinate system. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach; its applications are investigated. The method conservative providing conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Steady state solutions of the Euler equations are presented and discussed. The solutions include: low speed flow over a sphere, high speed flow over a slender body, supersonic flow through a duct, and supersonic internal/external flow interaction for an aircraft configuration at various angles of attack. The results demonstrate that the multiple grids approach along with the conservative interfacing is capable of computing the flows about the complex configurations where the use of a single grid system is not possible.
Kathong, Monchai↗
Ray trajectories in a torus: An application of MACSYMA to a complex numerical computation
The study of ray trajectories of plasma waves in a torodial geometry using MACSYMA is an example of how symbolic, numerical, and graphical facilities can be used in concert to accomplish a complex computational goal. Computational features of this study which are of particular significance include: the derivation of code (i.e. writing functions to generate program fragments), the use of array functions to simplify the specification of a numerical iteration scheme, and the graphical presentation of the results. Mathematically, this study originates in the solution of a linear inhomogeneous partial differential equation in 3 dimensions by the method of characteristics. While it is possible to describe this equation compactly by using vector notation, and by specifying the spatial variation of the coefficients in terms of intermediate parameters, the transformation of the equation into a form amenable to solution is very tedious. A MACSYMA program is presented for obtaining description of the rf field structure excited by a waveguide located at the edge of a toroidal plasma confinement device.
Kulp, J. L.↗
Iterative Demodulation and Decoding of Non-Square QAM
It has been shown that a non-square (NS) 2(sup 2n+1)-ary (where n is a positive integer) quadrature amplitude modulation [(NS)2(sup 2n+1)-QAM] has inherent memory that can be exploited to obtain coding gains. Moreover, it should not be necessary to build new hardware to realize these gains. The present scheme is a product of theoretical calculations directed toward reducing the computational complexity of decoding coded 2(sup 2n+1)-QAM. In the general case of 2(sup 2n+1)-QAM, the signal constellation is not square and it is impossible to have independent in-phase (I) and quadrature-phase (Q) mapping and demapping. However, independent I and Q mapping and demapping are desirable for reducing the complexity of computing the log likelihood ratio (LLR) between a bit and a received symbol (such computations are essential operations in iterative decoding). This is because in modulation schemes that include independent I and Q mapping and demapping, each bit of a signal point is involved in only one-dimensional mapping and demapping. As a result, the computation of the LLR is equivalent to that of a one-dimensional pulse amplitude modulation (PAM) system. Therefore, it is desirable to find a signal constellation that enables independent I and Q mapping and demapping for 2(sup 2n+1)-QAM.
Li, Lifang↗
Assessment of Quantum ML Applicability for Climate Actions: Comparison of the Variational Quantum Classifier and the Quantum Support Vector Classifier with Classical ML Models
Climate change refers to significant and long-term alterations in the Earth’s climate patterns, typically resulting from human activities that increase greenhouse gas emissions. Addressing climate change is not merely an option but a necessity, demanding creative solutions and efforts from individuals, researchers, communities, and governments. Despite the capabilities of machine learning (ML) with data-driven solutions promising to combat climate change-related problems, they face challenges stemming from traditional computational methods and prolonged training times, impeding their practical utility. Recent strides in quantum computing have permeated diverse domains, spanning from manufacturing engineering and pharmaceutical discovery to the latest frontier of detecting climate anomalies. With the potential to substantially reduce time and computational complexity, quantum computing shows promise in addressing climate change impacts. Its distinctive features will enable the concurrent exploration of expansive solution spaces, making it well-suited for analyzing extensive climate datasets, simulating intricate climate models, optimizing resource allocation, and discerning patterns in climate data for mitigation and adaptation endeavors. This study explores the potential of using Quantum machine learning (QML) techniques on climate and weather data obtained from NASA Giovannis. We used two QML algorithms, the Quantum Support Vector Classifier (QSVC) and the Variational Quantum Classifier (VQC) models, using the IBM Qiskit ML 0.7.2 ecosystem. We used an actual 127-Qubit IBM Quantum Computer (IBM 127-qubit Eagle) in this study. The methodology and results sections describe the experiences gained from applying and evaluating quantum ML results on climate and weather data obtained from NASA satellites as a novel practical application of quantum computing.
Earth Observational Data↗
Thermodynamic cost of computation, algorithmic complexity and the information metric
Algorithmic complexity is discussed as a computational counterpart to the second law of thermodynamics. It is shown that algorithmic complexity, which is a measure of randomness, sets limits on the thermodynamic cost of computations and casts a new light on the limitations of Maxwell's demon. Algorithmic complexity can also be used to define distance between binary strings.
Zurek, W. H.↗
Sign Problem in Tensor-Network Contraction
We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks with only positive entries has lower computational complexity as compared to tensor networks with general real or complex entries. This raises the question of how this transition in computational complexity manifests itself in the hardness of different tensor-network-contraction schemes. We pursue this question by studying random tensor networks with varying bias toward positive entries. First, we consider contraction via Monte Carlo sampling and find that the transition from hard to easy occurs when the tensor entries become predominantly positive; this can be understood as a tensor-network manifestation of the well-known negative-sign problem in quantum Monte Carlo. Second, we analyze the commonly used contraction based on boundary tensor networks. The performance of this scheme is governed by the number of correlations in contiguous parts of the tensor network (which by analogy can be thought of as entanglement). Remarkably, we find that the transition from hard to easy—i.e., from a volume-law to a boundary-law scaling of entanglement—already occurs for a slight bias of the tensor entries toward a positive mean, scaling inversely with the bond dimension D , and thus the problem becomes easy the earlier the larger D occurs. This is in contrast both to expectations and to the behavior found in Monte Carlo contraction, where the hardness at fixed bias increases with the bond dimension. To provide insight into this early breakdown of computational hardness and the accompanying entanglement transition, we construct an effective classical statistical-mechanical model that predicts a transition at a bias of the tensor entries of 1 / D , confirming our observations. We conclude by investigating the computational difficulty of computing expectation values of tensor-network wave functions (projected entangled-pair states, PEPSs) and find that in this setting, the complexity of entanglement-based contraction always remains low. We explain this by providing a local transformation that maps PEPS expectation values to a positive-valued tensor network. This not only provides insight into the origin of the observed boundary-law entanglement scaling but also suggests new approaches toward PEPS contraction based on positive decompositions. Published by the American Physical Society 2025
Chen, Jielun (ORCID:0000000178411545)↗
Efficient computation of the complex error function
Computation of complex error function
Gautschi, W.↗
Where are the parallel algorithms?
Four paradigms that can be useful in developing parallel algorithms are discussed. These include computational complexity analysis, changing the order of computation, asynchronous computation, and divide and conquer. Each is illustrated with an example from scientific computation, and it is shown that computational complexity must be used with great care or an inefficient algorithm may be selected.
Voigt, R. G.↗
A unifying framework for rigid multibody dynamics and serial and parallel computational issues
A unifying framework for various formulations of the dynamics of open-chain rigid multibody systems is discussed. Their suitability for serial and parallel processing is assessed. The framework is based on the derivation of intrinsic, i.e., coordinate-free, equations of the algorithms which provides a suitable abstraction and permits a distinction to be made between the computational redundancy in the intrinsic and extrinsic equations. A set of spatial notation is used which allows the derivation of the various algorithms in a common setting and thus clarifies the relationships among them. The three classes of algorithms viz., O(n), O(n exp 2) and O(n exp 3) or the solution of the dynamics problem are investigated. Researchers begin with the derivation of O(n exp 3) algorithms based on the explicit computation of the mass matrix and it provides insight into the underlying basis of the O(n) algorithms. From a computational perspective, the optimal choice of a coordinate frame for the projection of the intrinsic equations is discussed and the serial computational complexity of the different algorithms is evaluated. The three classes of algorithms are also analyzed for suitability for parallel processing. It is shown that the problem belongs to the class of N C and the time and processor bounds are of O(log2/2(n)) and O(n exp 4), respectively. However, the algorithm that achieves the above bounds is not stable. Researchers show that the fastest stable parallel algorithm achieves a computational complexity of O(n) with O(n exp 4), respectively. However, the algorithm that achieves the above bounds is not stable. Researchers show that the fastest stable parallel algorithm achieves a computational complexity of O(n) with O(n exp 2) processors, and results from the parallelization of the O(n exp 3) serial algorithm.
Fijany, Amir↗
Leveraging dendritic complexity for neuromorphic computing
Abstract Beyond-von Neumann computing approaches are necessary to sustain the growth of microelectronics and the increasing appetite for artificial intelligence/machine learning algorithms. Neuromorphic computing is an emerging paradigm that takes inspiration from the brain to provide a path forward to improve the computational efficiency and computational density of next-generation computing architectures. In nature, we observe brains performing complex computations with a much smaller energy footprint than conventional computing approaches. Current neuromorphic systems are focused primarily on scalability, namely, increasing the number of computational units (neurons) and connections between units (synapses). However, for brain-like cognition and efficiency in next-generation computing hardware, we need increased complexity in function, as well as improved connection density for scalability. Here, we present our work that aims to incorporate dendrites for ‘compute-on-wire’ in neuromorphic architectures to increase the computational complexity (e.g. number of programmable parameters, nonlinear dynamics) as well as computational efficiency (energy/compute) of artificial neural networks (ANNs). We do this by showcasing neuromorphic dendrite elements that can be leveraged for various applications. We will present examples of neuroscience-inspired direction-selective circuits and an ANN with active dendrites leveraging shunting inhibition. We also demonstrate the benefits of using dendrites in deep neural networks. To conclude, we discuss how we can utilize emerging hardware devices in these systems and design next-generation neuromorphic architectures with dendrites.
Cardwell, Suma G. (ORCID:0000000226575545)↗
A new fast algorithm for computing a complex number: Theoretic transforms
A high-radix fast Fourier transformation (FFT) algorithm for computing transforms over GF(sq q), where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.
Reed, I. S.↗
On the recognition of complex structures: Computer software using artificial intelligence applied to pattern recognition
An approach to simultaneous interpretation of objects in complex structures so as to maximize a combined utility function is presented. Results of the application of a computer software system to assign meaning to regions in a segmented image based on the principles described in this paper and on a special interactive sequential classification learning system, which is referenced, are demonstrated.
Yakimovsky, Y.↗
Ways of achieving continuous service from computers
This paper outlines the methods used in the real-time computer complex to keep computers operating. Methods include selectover, high-speed restart, and low-speed restart. The hardware and software needed to implement these methods is discussed as well as the system recovery facility, alternate device support, and timeout. In general, methods developed while supporting the Gemini, Apollo, and Skylab space missions are presented.
Quinn, M. J., Jr.↗
Estimation of spares
Simplified technique to determine the number of spare parts required for a given risk level employs shrot-cut approximations in lieu of computer-assisted or complex computational analyses.
Mezzacappa, M. A.↗
A time-parallel multiple-shooting method for large-scale quantum optimal control
Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. Further, this enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Shock diffraction computations over complex structures
This work contains the results of a study aimed at the development of two- and three-dimensional numerical procedures for computing the flowfield generated by the interaction of a blast wave and a rigid body. A number of numerical procedures were applied to two-dimensional problems including both implicit and explicit algorithms. Each was tried on the blast wave-cylinder interaction problem. MacCormack's (1969) method with added fourth-order dissipation yielded the best results and was then applied to the blast wave-truck interaction problems in two dimensions. MacCormack's method was also used in three dimensions to determine the flowfield that results when a blast wave strikes a rectangular parallelepiped at an arbitrary angle. Both the twoand three-dimensional computations were compared with experiments in a number of ways. Two dimensional density contours show qualitative agreement for shock front location and Mach stem formation with spark shadowgraphs taken in a shock tube. Pressure-time histories indicate good quantitative agreement between theory and experiment both in two- and three-dimensions.
Mark, A.↗
Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach
This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.
Aguilo, Miguel A.↗