A Complexity Theoretic Perspective on Robustness Analysis
The purpose of the paper is to present the steps that have been taken towards an algorithm theory of stability and robustness.
Algorithm Stability Robustness↗
SEARCH · Engineering Papers
Results for “algorithm complexity analysis”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
RNAseq-based transcriptome assembly of Clostridium acetobutylicum for functional genome annotation and discovery
Accurate genome annotations are essential in modern biology and biotechnology, yet they are still largely based on genome sequencing and comparative analyses. We show that the Clostridium acetobutylicum genome annotation can be markedly improved by integrating bioinformatic predictions with RNA sequencing (RNAseq) data. Samples were acquired under butanol, butyrate, and unstressed treatments across various growth conditions. Analysis of an initial assembly revealed errors due to background signals and limitations of assembly algorithms. Hurdles for RNAseq transcriptome mapping include optimizing library complexity and sequencing depth, yet most studies report low sequencing depth and ignore the effect of ribosomal RNA abundance. An integrative analysis was developed to combine motif predictions, single-nucleotide resolution sequencing depth, and library complexity to resolve difficulties in assembly curation. This minimized false positive error and determined gene boundaries, in some cases, to the exact base-pair of prior studies. This will be the first strand-specific transcriptome assembly in a Clostridium organism.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Analyzing Prospects for Quantum Advantage in Topological Data Analysis
Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024
97 MATHEMATICS AND COMPUTING↗
Discrete Fourier Transform Analysis in a Complex Vector Space
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
Dean, Bruce H.↗
Impact of cyber attacks on distributed compressive sensing based state estimation in power distribution grids
Modern power distribution grids suffer from multiple vulnerabilities due to the tight integration between the physical system and the cyber infrastructure. Sophisticated and malicious cyber attacks continue to adversely impact the grid operation leading to performance degradation, service interruption, and grid failure. State estimation plays an essential role in grid monitoring and advancing cyber-attack situational awareness. In this regard, this paper first proposes a distributed compressive sensing (CS) state estimation approach for an unobservable distribution grid. Further, the proposed distributed CS approach divides the distribution grid into sub-areas to perform local state estimation. Then an alternating direction method of multipliers (ADMM) based iterative information exchange among neighboring areas is employed to complete the estimation process. In this estimation process, the impact of loss of measurement data, false data injection (FDI), replay, and neighborhood cyber-attacks is analyzed. Extensive simulations are performed on the IEEE 37-bus and IEEE 123-bus standard networks to demonstrate the algorithm’s robustness to the aforementioned cyber-attacks. A quantitative analysis of computational complexity and simulation time of the distributed CS based approach is also presented.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Data recording and processing for speckle image reconstruction
Image reconstruction from astronomical speckle data using the Knox-Thompson algorithm has now been extensively demonstrated as feasible through analysis and computer simulations. Experimental verification of the technique and its implementation for astronomy places stringent constraints on the recording system and requires complex processing algorithms to handle the many experimental details. In this paper we describe a video recording system specifically designed for the requirements of speckle imaging. This system has been built and tested, yielding high quality image reconstructions from a laboratory-atmospheric simulator for a wide range of input light levels and test objects.
Nisenson, P.↗
Quantum algorithm to simulate Lindblad master equations
We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for the Lindblad master equation, achieved by decomposing the dynamics into dissipative and Hamiltonian components and replacing the dissipative segments with randomly compiled, easily implementable elements. The sampling approach eliminates the need for ancillary qubits to simulate the dissipation process and reduces the gate complexity in terms of the number of jump operators. We provide a rigorous performance analysis of the algorithm. We also extend the algorithm to time-dependent Lindblad equations, generalize the family of Markovian master equations it can be applied to, and explore applications beyond the Markovian noise model. A new error bound, in terms of the diamond norm, for second-order product formulas for time-dependent Liouvillians is provided that might be of independent interest. Published by the American Physical Society 2025
Borras, Evan (ORCID:000900017709037X)↗
On the equivalence of Gaussian elimination and Gauss-Jordan reduction in solving linear equations
A novel general approach to round-off error analysis using the error complexity concepts is described. This is applied to the analysis of the Gaussian Elimination and Gauss-Jordan scheme for solving linear equations. The results show that the two algorithms are equivalent in terms of our error complexity measures. Thus the inherently parallel Gauss-Jordan scheme can be implemented with confidence if parallel computers are available.
Tsao, Nai-Kuan↗
Parallel algorithms for placement and routing in VLSI design
The computational requirements for high quality synthesis, analysis, and verification of very large scale integration (VLSI) designs have rapidly increased with the fast growing complexity of these designs. Research in the past has focused on the development of heuristic algorithms, special purpose hardware accelerators, or parallel algorithms for the numerous design tasks to decrease the time required for solution. Two new parallel algorithms are proposed for two VLSI synthesis tasks, standard cell placement and global routing. The first algorithm, a parallel algorithm for global routing, uses hierarchical techniques to decompose the routing problem into independent routing subproblems that are solved in parallel. Results are then presented which compare the routing quality to the results of other published global routers and which evaluate the speedups attained. The second algorithm, a parallel algorithm for cell placement and global routing, hierarchically integrates a quadrisection placement algorithm, a bisection placement algorithm, and the previous global routing algorithm. Unique partitioning techniques are used to decompose the various stages of the algorithm into independent tasks which can be evaluated in parallel. Finally, results are presented which evaluate the various algorithm alternatives and compare the algorithm performance to other placement programs. Measurements are presented on the parallel speedups available.
Brouwer, Randall Jay↗
Scaling the SciDAC QuantOm Workflow
As part of the Scientific Discovery through Advanced Computing (SciDAC) program, the Quantum Chromodynamics Nuclear Tomography (QuantOM) project aims to analyze data from Deep Inelastic Scattering (DIS) experiments conducted at Jefferson Lab and the upcoming Electron Ion Collider. The DIS data analysis is performed on an event-level by combining the input from theoretical and experimental nuclear physics into a single, composable workflow. The optimization itself (I.e. fitting the experimental data with theoretical predictions) is carried out by a machine / deep learning algorithm. The size of the acquired DIS data as well as the complexity of the workflow itself require that the analysis is performed across multiple GPUs on high performance computing systems, such as Polaris at Argonne National Laboratory. This presentation discusses the novelties and challenges that came along with parallelizing this workflow. Recent results are compared to common distributed training techniques.
Lersch, Daniel↗
Modeling L 2,3 -edge X-ray absorption spectroscopy with linear response exact two-component relativistic time-dependent density functional theory
X-ray absorption spectroscopy (XAS) is a powerful tool that can provide physical insights into element-specific chemical processes and reactivities. Although relativistic time-dependent density functional theory (TDDFT) has been previously applied to model the L-edge region in XAS, there has not been a more comprehensive study of the choices of basis sets and density functional kernels available for variational relativistic excited state methods. In this work, we introduce the implementation of the generalized preconditioned locally harmonic residual algorithm to solve the complex-valued relativistic TDDFT for modeling the L-edge X-ray absorption spectra. Further, we investigate the L 2,3 -edge spectra of a series of molecular complexes using relativistic linear response TDDFT with a hybrid iterative diagonalization algorithm. A systematic error analysis was carried out with a focus on the energetics, intensities, and magnitude of L 2 –L 3 splitting compared to experiments. Additionally, the results from relativistic TDDFT calculations are compared to those computed using other theoretical methods, and the multideterminantal effects on the L-edge XAS were investigated.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
ExTreeM: Scalable Augmented Merge Tree Computation via Extremum Graphs
Over the last decade merge trees have been proven to support a plethora of visualization and analysis tasks since they effectively abstract complex datasets. Here, this paper describes the ExTreeM-Algorithm: A scalable algorithm for the computation of merge trees via extremum graphs. The core idea of ExTreeM is to first derive the extremum graph G of an input scalar field f defined on a cell complex K, and subsequently compute the unaugmented merge tree of f on G instead of K; which are equivalent. Any merge tree algorithm can be carried out significantly faster on G, since K in general contains substantially more cells than G. To further speed up computation, ExTreeM includes a tailored procedure to derive merge trees of extremum graphs. The computation of the fully augmented merge tree, i.e., a merge tree domain segmentation of K, can then be performed in an optional post-processing step. All steps of ExTreeM consist of procedures with high parallel efficiency, and we provide a formal proof of its correctness. Our experiments, performed on publicly available datasets, report a speedup of up to one order of magnitude over the state-of-the-art algorithms included in the TTK and VTK-m software libraries, while also requiring significantly less memory and exhibiting excellent scaling behavior.
97 MATHEMATICS AND COMPUTING↗
Evaluation of Hybrid FPOG Applications in Regulated and Deregulated Markets Using HERON
Recent changes in the U.S. energy market, such as low natural gas prices and increased electricity production for variable renewable energy (VRE) sources, have led to an economic crisis for existing light-water reactor (LWR) nuclear power plants (NPP). Many owners and operators of LWRs have elected to decommission these plants rather than continue using them as consistent sources of clean baseload power. This has led to exploration of various possibilities to increase the economic viability of these units, including market restructuring to monetize benefits LWRs already provide to the grid through ancillary markets, load following and economic dispatch, and possible integration of secondary systems directly to the NPP for production of additional products through technologies such as hydrogen electrolysis or water desalination. Previous studies have considered the technologies associated with these Integrated Energy Systems (IES) activities, and the analysis of markets for these secondary products. To analyze the economic viability of various system configurations including IES, especially given the uncertainty surrounding load demand, electricity prices, and the availability of VRE resources, the stochastic technoeconomic analysis package HERON (Heuristic Energy Resource Optimization Network) was released earlier this year as an extension of the risk analysis framework RAVEN (Risk Analysis Virtual Environment). HERON focuses foremost on making the complex uncertainty quantification analysis tools approachable for energy systems analysts, also providing general dispatch optimization algorithms for those workflows. HERON continues to be improved and tested as a significant part of the IES viability analyses performed in this work. HERON is not a capacity expansion model. To consider market and grid energy system development in a variety of scenarios, HERON is best used in coupling with modelling tools such as US-REGEN, which sacrifice some of the uncertainty analysis and resolution of HERON's modelling for the ability to efficiently predict the change in the grid energy system's profile due to economic drivers over decades. HERON can then use this information to explore the economic viability of introducing changes to the predicted outcomes, such as the introduction of an IES. In this work, experts at EPRI using US-REGEN provide six projection scenarios for use in HERON stochastic technoeconomic analysis (STEA) in considering the options available for increasing LWR economic viability through introduction of a hydrogen-centric IES using a high-temperature steam electrolysis plant (HTSE), hydrogen storage, and a constant-rate contracted hydrogen consumer. The results obtained are differential in nature; they do not report expected profits for any configuration, but rather report on the possible increase in the NPV of a configuration with respect to a baseline no-IES configuration. Due to the uncertainty captured in the variable net load of the systems, there is likewise uncertainty in the mean values reported. We consider this viability both in terms of a regulated market, where the energy producers and IES are owned and operated by single entity, as well as a deregulated market, where the IES chooses its bid for electricity generation and is then dispatched by the grid system operator. Results indicate that for deregulated markets, the inclusion of the IES is often statistically beneficial. This is especially true in policies that are not favorable towards nuclear, as nuclear is less often dispatched and is forced to deal with frequent idle capacity. In the nominal case as well as the case of carbon tax policies, inclusion of the IES clearly benefited the economic performance of the NPP. In the regulated case, however, there was a trend towards minimizing the IES, likely due to the optimal sizing performed by US-REGEN of the NPP within the system as well as the lack of penalty for idle capacity at the NPP in the regulated market analyses.
99 GENERAL AND MISCELLANEOUS↗
Monitoring and Acquisition Real-time System (MARS)
MARS is a graphical user interface (GUI) written in MATLAB and Java, allowing the user to configure and control the Scalable Parallel Architecture for Real-Time Acquisition and Analysis (SPARTAA) data acquisition system. SPARTAA not only acquires data, but also allows for complex algorithms to be applied to the acquired data in real time. The MARS client allows the user to set up and configure all settings regarding the data channels attached to the system, as well as have complete control over starting and stopping data acquisition. It provides a unique "Test" programming environment, allowing the user to create tests consisting of a series of alarms, each of which contains any number of data channels. Each alarm is configured with a particular algorithm, determining the type of processing that will be applied on each data channel and tested against a defined threshold. Tests can be uploaded to SPARTAA, thereby teaching it how to process the data. The uniqueness of MARS is in its capability to be adaptable easily to many test configurations. MARS sends and receives protocols via TCP/IP, which allows for quick integration into almost any test environment. The use of MATLAB and Java as the programming languages allows for developers to integrate the software across multiple operating platforms.
Holland, Corbin↗
QuaSiMo: A composable library to program hybrid workflows for quantum simulation
Abstract A composable design scheme is presented for the development of hybrid quantum/classical algorithms and workflows for applications of quantum simulation. The proposed object‐oriented approach is based on constructing an expressive set of common data structures and methods that enables programming of a broad variety of complex hybrid quantum simulation applications. The abstract core of the scheme is distilled from the analysis of the current quantum simulation algorithms. Subsequently, it allows synthesis of new hybrid algorithms and workflows via the extension, specialisation, and dynamic customisation of the abstract core classes defined by the proposed design. The design scheme is implemented using the hardware‐agnostic programming language QCOR into the QuaSiMo library. To validate the implementation, the authors test and show its utility on commercial quantum processors from IBM and Rigetti, running some prototypical quantum simulations.
97 MATHEMATICS AND COMPUTING↗
Implementation and operation of three fractal measurement algorithms for analysis of remote-sensing data
Fractal geometry is increasingly becoming a useful tool for modeling natural phenomena. As an alternative to Euclidean concepts, fractals allow for a more accurate representation of the nature of complexity in natural boundaries and surfaces. The purpose of this paper is to introduce and implement three algorithms in C code for deriving fractal measurement from remotely sensed data. These three methods are: the line-divider method, the variogram method, and the triangular prism method. Remote-sensing data acquired by NASA's Calibrated Airborne Multispectral Scanner (CAMS) are used to compute the fractal dimension using each of the three methods. These data were obtained as a 30 m pixel spatial resolution over a portion of western Puerto Rico in January 1990. A description of the three methods, their implementation in PC-compatible environment, and some results of applying these algorithms to remotely sensed image data are presented.
Jaggi, S.↗
Review of LMIs, Interior Point Methods, Complexity Theory, and Robustness Analysis
From end of intro: ...We would like to show that for certain problems in systems and control theory, there exist algorithms for which corresponding (xi) can be viewed as a certain measure of robustness, e.g., stability margin.
control systems control system analysis↗