Chlorophyll dynamics from Sentinel-3 using an optimized algorithm for enhanced ecological monitoring in complex urban estuarine waters
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Jonathan Sherman↗
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Evaluating the seasonal and decadal performance of red band difference algorithms for chlorophyll in an optically complex estuary with winter and summer blooms
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Fernanda Henderikx Freitas↗
FPT Algorithm for Two-Dimensional Cyclic Convolutions
Fast-polynomial-transform (FPT) algorithm computes two-dimensional cyclic convolution of two-dimensional arrays of complex numbers. New algorithm uses cyclic polynomial convolutions of same length. Algorithm regular, modular, and expandable.
Truong, Trieu-Kie↗
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↗
Symbolic Solution of Linear Differential Equations
An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.
Feinberg, R. B.↗
A Regression Method for Comparing Launch Zone Ranges Derived From Different Sources
In modern fighter aircraft air-to-air missile launch acceptable ranges (LARs) are provided to the pilot for his launch decision. These LARs are calculated in the avionic software, using very simple algebraic equations and algorithms, that attempt to model complex missile behavior. Frequently these algorithms are revised to reflect inaccuracies discovered, when comparisons are made with missile six degree-of-freedom (6-DOF) simulations. The process of modifying this software has become expensive. In the past, these simple LAR generators were modified based only on subjective judgmental approach, with little regard to the missile range design limits. With reduced budgets a more rational methodology should be taken to assess whether or not simple fighter LAR generators need to be modified. Any LAR generator can produce large amounts of range (minimum and maximum) data over the board engagement limits of modem fighter and air-to-air missiles. This infinite population lends itself to some statistical methodology to access simple LAR accuracy and the need for software modification. The methodology should produce statistical parameters for use in the decision making process of modifying a simple fighter LAR generator. This paper presents a regression method, based on a missile range design limit philosophy. Acceptance criteria from the regression method are given that provide simple statistical parameters to aid in this decision making process.
Flight Testing↗
Computing Bounds on Resource Levels for Flexible Plans
A new algorithm efficiently computes the tightest exact bound on the levels of resources induced by a flexible activity plan (see figure). Tightness of bounds is extremely important for computations involved in planning because tight bounds can save potentially exponential amounts of search (through early backtracking and detection of solutions), relative to looser bounds. The bound computed by the new algorithm, denoted the resource-level envelope, constitutes the measure of maximum and minimum consumption of resources at any time for all fixed-time schedules in the flexible plan. At each time, the envelope guarantees that there are two fixed-time instantiations one that produces the minimum level and one that produces the maximum level. Therefore, the resource-level envelope is the tightest possible resource-level bound for a flexible plan because any tighter bound would exclude the contribution of at least one fixed-time schedule. If the resource- level envelope can be computed efficiently, one could substitute looser bounds that are currently used in the inner cores of constraint-posting scheduling algorithms, with the potential for great improvements in performance. What is needed to reduce the cost of computation is an algorithm, the measure of complexity of which is no greater than a low-degree polynomial in N (where N is the number of activities). The new algorithm satisfies this need. In this algorithm, the computation of resource-level envelopes is based on a novel combination of (1) the theory of shortest paths in the temporal-constraint network for the flexible plan and (2) the theory of maximum flows for a flow network derived from the temporal and resource constraints. The measure of asymptotic complexity of the algorithm is O(N O(maxflow(N)), where O(x) denotes an amount of computing time or a number of arithmetic operations proportional to a number of the order of x and O(maxflow(N)) is the measure of complexity (and thus of cost) of a maximumflow algorithm applied to an auxiliary flow network of 2N nodes. The algorithm is believed to be efficient in practice; experimental analysis shows the practical cost of maxflow to be as low as O(N1.5). The algorithm could be enhanced following at least two approaches. In the first approach, incremental subalgorithms for the computation of the envelope could be developed. By use of temporal scanning of the events in the temporal network, it may be possible to significantly reduce the size of the networks on which it is necessary to run the maximum-flow subalgorithm, thereby significantly reducing the time required for envelope calculation. In the second approach, the practical effectiveness of resource envelopes in the inner loops of search algorithms could be tested for multi-capacity resource scheduling. This testing would include inner-loop backtracking and termination tests and variable and value-ordering heuristics that exploit the properties of resource envelopes more directly.
Muscvettola, Nicola↗
Application of Sparse Identification of Nonlinear Dynamics for Physics-Informed Learning
Advances in machine learning and deep neural networks has enabled complex engineering tasks like image recognition, anomaly detection, regression, and multi-objective optimization, to name but a few. The complexity of the algorithm architecture, e.g., the number of hidden layers in a deep neural network, typically grows with the complexity of the problems they are required to solve, leaving little room for interpreting (or explaining) the path that results in a specific solution. This drawback is particularly relevant for autonomous aerospace and aviation systems, where certifications require a complete understanding of the algorithm behavior in all possible scenarios. Including physics knowledge in such data-driven tools may improve the interpretability of the algorithms, thus enhancing model validation against events with low probability but relevant for system certification. Such events include, for example, spacecraft or aircraft sub-system failures, for which data may not be available in the training phase. This paper investigates a recent physics-informed learning algorithm for identification of system dynamics, and shows how the governing equations of a system can be extracted from data using sparse regression. The learned relationships can be utilized as a surrogate model which, unlike typical data-driven surrogate models, relies on the learned underlying dynamics of the system rather than large number of fitting parameters. The work shows that the algorithm can reconstruct the differential equations underlying the observed dynamics using a single trajectory when no uncertainty is involved. However, the training set size must increase when dealing with stochastic systems, e.g., nonlinear dynamics with random initial conditions.
Corbetta, Matteo↗
Parallel processing for digital picture comparison
In picture processing an important problem is to identify two digital pictures of the same scene taken under different lighting conditions. This kind of problem can be found in remote sensing, satellite signal processing and the related areas. The identification can be done by transforming the gray levels so that the gray level histograms of the two pictures are closely matched. The transformation problem can be solved by using the packing method. Researchers propose a VLSI architecture consisting of m x n processing elements with extensive parallel and pipelining computation capabilities to speed up the transformation with the time complexity 0(max(m,n)), where m and n are the numbers of the gray levels of the input picture and the reference picture respectively. If using uniprocessor and a dynamic programming algorithm, the time complexity will be 0(m(3)xn). The algorithm partition problem, as an important issue in VLSI design, is discussed. Verification of the proposed architecture is also given.
Cheng, H. D.↗
Aerocapture Guidance Algorithm Comparison Campaign
The aerocapture is a promising technique for the future human interplanetary missions. The Mars Sample Return was initially based on an insertion by aerocapture. A CNES orbiter Mars Premier was developed to demonstrate this concept. Mainly due to budget constraints, the aerocapture was cancelled for the French orbiter. A lot of studies were achieved during the three last years to develop and test different guidance algorithms (APC, EC, TPC, NPC). This work was shared between CNES and NASA, with a fruitful joint working group. To finish this study an evaluation campaign has been performed to test the different algorithms. The objective was to assess the robustness, accuracy, capability to limit the load, and the complexity of each algorithm. A simulation campaign has been specified and performed by CNES, with a similar activity on the NASA side to confirm the CNES results. This evaluation has demonstrated that the numerical guidance principal is not competitive compared to the analytical concepts. All the other algorithms are well adapted to guaranty the success of the aerocapture. The TPC appears to be the more robust, the APC the more accurate, and the EC appears to be a good compromise.
Rousseau, Stephane↗
Improved algorithms for mapping pipelined and parallel computations
Recent work on the problem of mapping pipelined or parallel computations onto linear array, shared memory, and host-satellite systems is extended. It is shown how these problems can be solved even more efficiently when computation module execution times are bounded from below, intermodule communication times are bounded from above, and the processors satisfy certain homogeneity constraints. The improved algorithms have significantly lower time and space complexities than the more general algorithms: in one case, an O(nm3) time algorithm for mapping m modules onto n processors is replaced with an O(nm log m) time algorithm, and the space requirements are reduced from O(nm2) to O(m). Run-time complexity is reduced further with parallel mapping algorithms based on these improvements, which run on the architectures for which they create mappings.
Nicol, David M.↗
Evaluating scheduling algorithms for traffic with heterogeneous performance objectives
Two types of network traffic are considered: traffic with deadlines, for which the most important performance objective is based on loss rate, and packets without deadlines, for which the most important performance objective is based on mean delay. An optimal scheduling algorithm is presented to minimize weighted loss rate and weighted mean delay in the queues that form at the switches and at the network access points of a packet-switched network, where weights reflect the relative importance of packets. Although not practical for implementation, the algorithm is intended as a standard for the comparison of the performance of other scheduling algorithms. The algorithm is more general and lower computational complexity than previously published algorithms, enabling performance evaluation of some important scenarios that could not previously have been considered. Using the optimal performance results of this algorithm, the performance of the first-come-first-served, static priority, and earliest deadline first scheduling algorithms is evaluated. The results suggest that network efficiency could be improved by using a more sophisticated heuristic scheduling algorithm rather than one of the aforementioned algorithms.
Peha, Jon M.↗
Empirical study of parallel LRU simulation algorithms
This paper reports on the performance of five parallel algorithms for simulating a fully associative cache operating under the LRU (Least-Recently-Used) replacement policy. Three of the algorithms are SIMD, and are implemented on the MasPar MP-2 architecture. Two other algorithms are parallelizations of an efficient serial algorithm on the Intel Paragon. One SIMD algorithm is quite simple, but its cost is linear in the cache size. The two other SIMD algorithm are more complex, but have costs that are independent on the cache size. Both the second and third SIMD algorithms compute all stack distances; the second SIMD algorithm is completely general, whereas the third SIMD algorithm presumes and takes advantage of bounds on the range of reference tags. Both MIMD algorithm implemented on the Paragon are general and compute all stack distances; they differ in one step that may affect their respective scalability. We assess the strengths and weaknesses of these algorithms as a function of problem size and characteristics, and compare their performance on traces derived from execution of three SPEC benchmark programs.
Carr, Eric↗
On the accuracy of solving triangular systems in parallel
An error complexity analysis of two algorithms for solving a unit-diagonal triangular system is given. The results show that the unusual sequential algorithm is optimal in terms of having the minimal maximum and cumulative error complexity measures. The parallel algorithm described by Sameh and Brent is shown to be essentially equivalent to the optimal sequential one. Some numerical experiments are also taught.
Tsao, Nai-Kuan↗
Self-Avoiding Walks over Adaptive Triangular Grids
In this paper, we present a new approach to constructing a "self-avoiding" walk through a triangular mesh. Unlike the popular approach of visiting mesh elements using space-filling curves which is based on a geometric embedding, our approach is combinatorial in the sense that it uses the mesh connectivity only. We present an algorithm for constructing a self-avoiding walk which can be applied to any unstructured triangular mesh. The complexity of the algorithm is O(n x log(n)), where n is the number of triangles in the mesh. We show that for hierarchical adaptive meshes, the algorithm can be easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.
Heber, Gerd↗
Quantum Adiabatic Algorithms and Large Spin Tunnelling
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.
Boulatov, A.↗
Evaluating Algorithm Performance Metrics Tailored for Prognostics
Prognostics has taken a center stage in Condition Based Maintenance (CBM) where it is desired to estimate Remaining Useful Life (RUL) of the system so that remedial measures may be taken in advance to avoid catastrophic events or unwanted downtimes. Validation of such predictions is an important but difficult proposition and a lack of appropriate evaluation methods renders prognostics meaningless. Evaluation methods currently used in the research community are not standardized and in many cases do not sufficiently assess key performance aspects expected out of a prognostics algorithm. In this paper we introduce several new evaluation metrics tailored for prognostics and show that they can effectively evaluate various algorithms as compared to other conventional metrics. Specifically four algorithms namely; Relevance Vector Machine (RVM), Gaussian Process Regression (GPR), Artificial Neural Network (ANN), and Polynomial Regression (PR) are compared. These algorithms vary in complexity and their ability to manage uncertainty around predicted estimates. Results show that the new metrics rank these algorithms in different manner and depending on the requirements and constraints suitable metrics may be chosen. Beyond these results, these metrics offer ideas about how metrics suitable to prognostics may be designed so that the evaluation procedure can be standardized. 1
Saxena, Abhinav↗
Performance Analysis of a Hardware Implemented Complex Signal Kurtosis Radio-Frequency Interference Detector
Radio-frequency interference (RFI) is a known problem for passive remote sensing as evidenced in the L-band radiometers SMOS, Aquarius and more recently, SMAP. Various algorithms have been developed and implemented on SMAP to improve science measurements. This was achieved by the use of a digital microwave radiometer. RFI mitigation becomes more challenging for microwave radiometers operating at higher frequencies in shared allocations. At higher frequencies larger bandwidths are also desirable for lower measurement noise further adding to processing challenges. This work focuses on finding improved RFI mitigation techniques that will be effective at additional frequencies and at higher bandwidths. To aid the development and testing of applicable detection and mitigation techniques, a wide-band RFI algorithm testing environment has been developed using the Reconfigurable Open Architecture Computing Hardware System (ROACH) built by the Collaboration for Astronomy Signal Processing and Electronics Research (CASPER) Group. The testing environment also consists of various test equipment used to reproduce typical signals that a radiometer may see including those with and without RFI. The testing environment permits quick evaluations of RFI mitigation algorithms as well as show that they are implementable in hardware. The algorithm implemented is a complex signal kurtosis detector which was modeled and simulated. The complex signal kurtosis detector showed improved performance over the real kurtosis detector under certain conditions. The real kurtosis is implemented on SMAP at 24 MHz bandwidth. The complex signal kurtosis algorithm was then implemented in hardware at 200 MHz bandwidth using the ROACH. In this work, performance of the complex signal kurtosis and the real signal kurtosis are compared. Performance evaluations and comparisons in both simulation as well as experimental hardware implementations were done with the use of receiver operating characteristic (ROC) curves.
radiometers↗